Mister Exam
Other calculators
- Derivative of a implicit defined function
- Curve tracing functions Step by Step
- Surface Plot
- Canonical form of a curve
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How to use it?
- Plot:
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-1-(36*(x^2-y^2+5*x+6)-(36*x+132)*(2*x+5))/((x^2-y^2+5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
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x^2+(y-cbrt(x^2))^2=1
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x^2+x*y^2=1
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sqrt(x)+sqrt(y)=1
- Canonical form:
- x+2y+z,y-z-x+y
- 4x1x2+x2^2+4x2x3+2x3^2-4x1-2x2-5=0
- u(xx)-4u(xy)+5u(yy)-3u(x)+u(y)+u=0
- 4x2+9y2–40x+36y+100=0.
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Identical expressions
- - one -(thirty-six *(x^ two -y^ two + five *x+ six)-(thirty-six *x+ one hundred and thirty-two)*(two *x+ five))/((x^ two -y^ two + five *x+ six)^ two + four *x^ two *y+ twenty-five *y^ two + twenty *x*y^ two)= zero
- minus 1 minus (36 multiply by (x squared minus y squared plus 5 multiply by x plus 6) minus (36 multiply by x plus 132) multiply by (2 multiply by x plus 5)) divide by ((x squared minus y squared plus 5 multiply by x plus 6) squared plus 4 multiply by x squared multiply by y plus 25 multiply by y squared plus 20 multiply by x multiply by y squared ) equally 0
- minus one minus (thirty minus six multiply by (x to the power of two minus y to the power of two plus five multiply by x plus six) minus (thirty minus six multiply by x plus one hundred and thirty minus two) multiply by (two multiply by x plus five)) divide by ((x to the power of two minus y to the power of two plus five multiply by x plus six) to the power of two plus four multiply by x to the power of two multiply by y plus twenty minus five multiply by y to the power of two plus twenty multiply by x multiply by y to the power of two) equally zero
- -1-(36*(x2-y2+5*x+6)-(36*x+132)*(2*x+5))/((x2-y2+5*x+6)2+4*x2*y+25*y2+20*x*y2)=0
- -1-36*x2-y2+5*x+6-36*x+132*2*x+5/x2-y2+5*x+62+4*x2*y+25*y2+20*x*y2=0
- -1-(36*(x²-y²+5*x+6)-(36*x+132)*(2*x+5))/((x²-y²+5*x+6)²+4*x²*y+25*y²+20*x*y²)=0
- -1-(36*(x to the power of 2-y to the power of 2+5*x+6)-(36*x+132)*(2*x+5))/((x to the power of 2-y to the power of 2+5*x+6) to the power of 2+4*x to the power of 2*y+25*y to the power of 2+20*x*y to the power of 2)=0
- -1-(36(x^2-y^2+5x+6)-(36x+132)(2x+5))/((x^2-y^2+5x+6)^2+4x^2y+25y^2+20xy^2)=0
- -1-(36(x2-y2+5x+6)-(36x+132)(2x+5))/((x2-y2+5x+6)2+4x2y+25y2+20xy2)=0
- -1-36x2-y2+5x+6-36x+1322x+5/x2-y2+5x+62+4x2y+25y2+20xy2=0
- -1-36x^2-y^2+5x+6-36x+1322x+5/x^2-y^2+5x+6^2+4x^2y+25y^2+20xy^2=0
- -1-(36*(x^2-y^2+5*x+6)-(36*x+132)*(2*x+5))/((x^2-y^2+5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=O
- -1-(36*(x^2-y^2+5*x+6)-(36*x+132)*(2*x+5)) divide by ((x^2-y^2+5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
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Similar expressions
- -1+(36*(x^2-y^2+5*x+6)-(36*x+132)*(2*x+5))/((x^2-y^2+5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
- -1-(36*(x^2-y^2+5*x+6)-(36*x-132)*(2*x+5))/((x^2-y^2+5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
- -1-(36*(x^2-y^2+5*x+6)-(36*x+132)*(2*x+5))/((x^2+y^2+5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
- -1-(36*(x^2-y^2+5*x+6)-(36*x+132)*(2*x+5))/((x^2-y^2+5*x+6)^2+4*x^2*y-25*y^2+20*x*y^2)=0
- 1-(36*(x^2-y^2+5*x+6)-(36*x+132)*(2*x+5))/((x^2-y^2+5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
- -1-(36*(x^2-y^2-5*x+6)-(36*x+132)*(2*x+5))/((x^2-y^2+5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
- -1-(36*(x^2-y^2+5*x+6)+(36*x+132)*(2*x+5))/((x^2-y^2+5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
- -1-(36*(x^2-y^2+5*x+6)-(36*x+132)*(2*x+5))/((x^2-y^2+5*x+6)^2-4*x^2*y+25*y^2+20*x*y^2)=0
- -1-(36*(x^2-y^2+5*x-6)-(36*x+132)*(2*x+5))/((x^2-y^2+5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
- -1-(36*(x^2-y^2+5*x+6)-(36*x+132)*(2*x+5))/((x^2-y^2+5*x-6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
- -1-(36*(x^2-y^2+5*x+6)-(36*x+132)*(2*x+5))/((x^2-y^2+5*x+6)^2+4*x^2*y+25*y^2-20*x*y^2)=0
- -1-(36*(x^2-y^2+5*x+6)-(36*x+132)*(2*x-5))/((x^2-y^2+5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
- -1-(36*(x^2-y^2+5*x+6)-(36*x+132)*(2*x+5))/((x^2-y^2-5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
- -1-(36*(x^2+y^2+5*x+6)-(36*x+132)*(2*x+5))/((x^2-y^2+5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
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What you mean?
- -(-(2*x + 5)*(36*x + 132) + 36*(x^2 + 5*x - y^2 + 6))/(4*x^2*y + 20*x*y^2 + 25*y^2 + (x^2 + 5*x - y^2 + 6)^2) - 1 = 0
- -(-(2*x + 5)*(36*x + 132) + 36*(x^2 + 5*x - y^2 + 6))/(20*x*y^2 + 4*x^(2*y) + 25*y^2 + (x^2 + 5*x - y^2 + 6)^2) - 1 = 0
- -(-(2*x + 5)*(36*x + 132) + 36*(x^2 + 5*x - y^2 + 6))/(20*x*y^2 + 4*x^(2*y + 25)*y^2 + (x^2 + 5*x - y^2 + 6)^2) - 1 = 0
- -(-(2*x + 5)*(36*x + 132) + 36*(x^2 + 5*x - y^2 + 6))/(20*x*y^2 + 4*x^(2*y + 25)*y^2 + (x^2 + 5*x - y^2 + 6)^2) - 1 = 0
You entered:
-1-(36*(x^2-y^2+5*x+6)-(36*x+132)*(2*x+5))/((x^2-y^2+5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
What you mean?
Plot -1-(36*(x^2-y^2+5*x+6)-(36*x+132)*(2*x+5))/((x^2-y^2+5*x+6)^2+4*x^2*y+25*y^2+20*x*y^2)=0
The solution
You have entered
[src]
/ 2 2 \
36*\x - y + 5*x + 6/ - (36*x + 132)*(2*x + 5)
-1 - ----------------------------------------------- = 0
2
/ 2 2 \ 2 2 2
\x - y + 5*x + 6/ + 4*x *y + 25*y + 20*x*y
$$-1 - \frac{- \left(2 x + 5\right) \left(36 x + 132\right) + 36 \left(\left(5 x + \left(x^{2} - y^{2}\right)\right) + 6\right)}{20 x y^{2} + \left(25 y^{2} + \left(4 x^{2} y + \left(\left(5 x + \left(x^{2} - y^{2}\right)\right) + 6\right)^{2}\right)\right)} = 0$$
The graph of the function
The graph
Examples of implicit functions
- Trigonometric functions
x^2*sin(y) + x*y - 1 = 0
- Power functions
x^2 + x*y^2 = 1
- Exponential functions
x^y = y^x
- In the form of infinity
(x^2 + y^2)^2 - 7*(x^2 - y^2)
- A galaxy
arctg(x/y) = x*y
- Curved square
x^4 + y^4 = x^2 + y^2
- Surface defined by an implicit function
x^4*y^3*z^2 + y^4*x^3*z = x^2*z^4 + y^2
- Mordell curve
y^2 = x^3 + 1
y^2 = x^3 + 5
y^2 = x^3 + 8
y^2 = x^3 + 12
- Deltoid
(x^2 + y^2)^2 + 18*(x^2 + y^2) = 8*x^3 - 24*y^2*x + 27
- Cartesian oval
(x^2 + y^2 - 2*x)^2 = x^2 + y^2
(x^2 + y^2 - 2*x)^2 = x^2 + y^2 + 1
(x^2 + y^2 - 2*x)^2 = x^2 + y^2 - 1
(x^2 + y^2 - 2*x)^2 = x^2 + y^2 + 1/20
(x^2 + y^2 - 3*x)^2 = 1/2
- Cassini oval
(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (3 / 5)^4
(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (4 / 5)^4
(x^2 + y^2)^2 - 2*(x^2 - y^2) = 0
(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (6 / 5)^4
(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (7 / 5)^4
(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (8 / 5)^4
- Cissoid
x*(x^2 + y^2) + 2/7*y^2 = 0
- Cissoid of Diocles
(x^2 + y^2)*x = 2*y^2 / 3
- Conchoid of de Sluze
(x - 1)*(x^2 + y^2) = x^2
- Conchoid of Dürer
2*y^2*(x^2 + y^2) - 10*y^2*(x + y) - 2*y^2 - 9*x^2 + 90*(x + y) - 144 = 0
- Trisectrix of Maclaurin
2*x*(x^2 + y^2) = (3*x^2 - y^2) / 2
- Cruciform curve
x^2*y^2 - 9*x^2 - 4*y^2 = 0
- Ampersand curve
(y^2 - x^2)*(x - 1)*(2*x - 3) = 4*(x^2 + y^2 - 2*x)
- Bean curve
x^4 + x^2*y^2 + y^4 = x*(x^2 + y^2)
- Bicuspid curve
(x^2 - 1)*(x - 1)^2 + (y^2 - 1)^2 = 0
- Bow curve
x^4 = x^2*y - y^3
- Spiric section
(x^2 + y^2 - 6)^2 = 16*(x^2 + 1)
- Crunode
y^2 - x^2*(x + 1) = 0
- Elkies trinomial curves
y^2 = x*(81*x^5 + 396*x^4 + 738*x^3 + 660*x^2 + 269*x + 48)
- Bicorn
y^2 * (1 - x^2) = (x^2 + 2*y - 1)^2
- Bifolium
(x^2 + y^2)^2 = 3*x^2*y
- Bitangents of quartic
144*(x^4 + y^4) - 225*(x^2 + y^2) + 350*x^2*y^2 + 81 = 0
- Bullet-nose curve
y^2 - 4*x^2 = x^2*y^2
- Semicubical parabola
y^2 - 4*x^3 = 0
- Serpentine curve
x^2*y + 4*y - 6*x = 0
- Folium of Descartes
x^3 + y^3 - 6*x*y = 0
- Trident curve
x*y + x^3 + x^2 + x = 1
- Tschirnhausen cubic
x^3 = 9*(x^2 - 3*y^2)
- Witch of Agnesi
y = 8 / (x^2 + 4)
- Devil's curve
y^2*(y^2 - 4) = x^2 * (x^2 - 9)
- Hippopede
(x^2 + y^2)^2 = 2*x^2 + y^2
- Kampyle of Eudoxus
x^4 = 4*(x^2 + y^2)
- Kappa curve
x^2*(x^2 + y^2) = 4*y^2
- Lemniscate of Gerono
x^4 - x^2 + y^2 = 0
- Lemniscate of Bernoulli
(x^2 + y^2)^2 = a^2*(x^2 - y^2)
- Limacon of Pascal
(x^2 + y^2 - 3*x)^2 = 4*(x^2 + y^2)
- Cardioid
(x^2 + y^2)^2 + 8*x*(x^2 + y^2) - 16*y^2 = 0
- Trisectris Pascal
4*(x^2 + y^2) = (x^2 + y^2 - 4*x)^2
- Squircle
x^4 + y^4 = 1
- Three leaf curve
(x^2 + y^2)*(y^2 + x*(x + 1)) = 4*x*y^2
- Astroid
x^(2/3) + y^(2/3) = 1
- Atriphtaloid
x^4 * (x^2 + y^2) - (2*x^2 - 3)^2 = 0
- Nephroid
(x^2 + y^2 - 4)^3 = 108*y^2
- Quadrifolium
(x^2 + y^2)^3 = 4 * (x^2 - y^2)^2
- Elliptic curve
y^2 = x^3 + 2*x + 5
- Bolza surface
y^2 = x^5 - x
- Butterfly curve
x^6 + y^6 = x^2
- Polynomial lemniscate
(x^2 + y^2)^2 = 2*(x^2 - y^2)
- Superellipse
x^(1/2) + y^(1/2) = 1
x^(3/2) + y^(3/2) = 1
- Hyperelliptic curve
y^2 = x^5 - 2*x^4 - 7*x^3 + 8*x^2
- Cochleoid
(x^2 + y^2)*atan(y/x) = 2*y
- Cycloid
x = 2*acos(1 - y/2) - sqrt(y*(2*2 - y))
- Pursuit curve
x = 1/4*(y^2 - ln(y)^2 - 1)
x = 1/3*(1/y - 1)
- Archimedean spiral
sqrt(x^2 + y^2) = 1/2 * atan(y/x) + 3
- Fermat's spiral
x/y = cot((x^2 + y^2)/4)
- Hyperbolic spiral
y/x = tan(2/sqrt(x^2 + y^2))
- Lituus
y/x = tan(2/(x^2 + y^2))
- Syntractrix
x + sqrt(1 - y^2) = ln([1 + sqrt(1 - y^2)]/y)/2
x + sqrt(1 - y^2) = 3*ln([1 + sqrt(1 - y^2)]/y)/2
- Tractrix
x = abs(ln([1 + sqrt(1 - y^2)]/y) - sqrt(1 - y^2))
- Viviani's curve
x = 2 - z^2/2
y = abs(z*sqrt(1 - z^2/4))
y = abs(sqrt(x*(2 - x)))
z = abs(sqrt(2*(2 - x)))
x - 1 = abs(sqrt(1 - y^2))
z^2 - 2 = abs(2*sqrt(1 - y^2))
- Fish curve
(2*x^2 + y^2)^2 - 2*sqrt(2)*x*(2*x^2 - 3*y^2) + 2*(y^2 - x^2) = 0
- Oblique strophoid
x^3 + x*y^2 - x^2 + y^2 = y*(x^2 + y^2 - 2*x)
- Two parallel straight lines
9x^2+12xy+4y^2-24x-16y+3=0
- Parabola
x^2-2xy+y^2-10x-6y+25=0
- Degenerate Ellipse
5x^2+4xy+y^2-6x-2y+2=0
- Ellipse
5*x^2+4*x*y+8*y^2+8*x+14*y+5=0
- Imaginary Ellipse
8063 - 250*y - 10*x + 50*x^2 + 50*y^2
- Ellipsoid
-243 - 216*z - 18*x + 4*y^2 + 25*x^2 + 36*z^2 + 16*x*y = 0
- Imaginary Ellipsoid
2*x^2+4*y^2+z^2-4*x*y-4*y-2*z+5=0
- Double Hyperboloid
x^2+y^2-z^2-2*x-2*y+2*z+2=0
- Elliptical Paraboloid
x^2+y^2-6*x+6*y-4*z+18=0
- Two Parallel Planes
x^2+4*y^2+9*z^2+4*x*y+12*y*z+6*x*z-4*x-8*y-12*z+3=0
Learn more about Implicit function
The above examples also contain:
- the modulus or absolute value: absolute(x) or |x|
-
square roots sqrt(x),
cubic roots cbrt(x) -
trigonometric functions:
sinus sin(x), cosine cos(x), tangent tan(x), cotangent ctan(x) - exponential functions and exponents exp(x)
-
inverse trigonometric functions:
arcsine asin(x), arccosine acos(x), arctangent atan(x), arccotangent acot(x) -
natural logarithms ln(x),
decimal logarithms log(x) -
hyperbolic functions:
hyperbolic sine sh(x), hyperbolic cosine ch(x), hyperbolic tangent and cotangent tanh(x), ctanh(x) -
inverse hyperbolic functions:
hyperbolic arcsine asinh(x), hyperbolic arccosinus acosh(x), hyperbolic arctangent atanh(x), hyperbolic arccotangent acoth(x) -
other trigonometry and hyperbolic functions:
secant sec(x), cosecant csc(x), arcsecant asec(x), arccosecant acsc(x), hyperbolic secant sech(x), hyperbolic cosecant csch(x), hyperbolic arcsecant asech(x), hyperbolic arccosecant acsch(x) -
rounding functions:
round down floor(x), round up ceiling(x) -
the sign of a number:
sign(x) -
for probability theory:
the error function erf(x) (integral of probability), Laplace function laplace(x) -
Factorial of x:
x! or factorial(x) - Gamma function gamma(x)
- Lambert's function LambertW(x)
- Trigonometric integrals: Si(x), Ci(x), Shi(x), Chi(x)
The insertion rules
The following operations can be performed
- 2*x
- - multiplication
- 3/x
- - division
- x^2
- - squaring
- x^3
- - cubing
- x^5
- - raising to the power
- x + 7
- - addition
- x - 6
- - subtraction
- Real numbers
- insert as 7.5, no 7,5
Constants
- pi
- - number Pi
- e
- - the base of natural logarithm
- i
- - complex number
- oo
- - symbol of infinity