Question
Solve the equation
Solve for x
Solve for y
x=∣y∣1x=−∣y∣1
Evaluate
9x2×4y2=36
Multiply the terms
36x2y2=36
Rewrite the expression
36y2x2=36
Divide both sides
36y236y2x2=36y236
Divide the numbers
x2=36y236
Divide the numbers
x2=y21
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±y21
Simplify the expression
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Evaluate
y21
To take a root of a fraction,take the root of the numerator and denominator separately
y21
Simplify the radical expression
y21
Simplify the radical expression
∣y∣1
x=±∣y∣1
Solution
x=∣y∣1x=−∣y∣1
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Testing for symmetry
Testing for symmetry about the origin
Testing for symmetry about the x-axis
Testing for symmetry about the y-axis
Symmetry with respect to the origin
Evaluate
9x2×4y2=36
Multiply the terms
36x2y2=36
To test if the graph of 36x2y2=36 is symmetry with respect to the origin,substitute -x for x and -y for y
36(−x)2(−y)2=36
Evaluate
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Evaluate
36(−x)2(−y)2
Multiply the terms
36x2(−y)2
Multiply the terms
36x2y2
36x2y2=36
Solution
Symmetry with respect to the origin
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Rewrite the equation
r=42csc2(2θ)r=−42csc2(2θ)
Evaluate
9x2×4y2=36
Evaluate
36x2y2=36
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
36(cos(θ)×r)2(sin(θ)×r)2=36
Factor the expression
36cos2(θ)sin2(θ)×r4=36
Simplify the expression
(36cos2(θ)−36cos4(θ))r4=36
Divide the terms
r4=cos2(θ)−cos4(θ)1
Simplify the expression
r4=4csc2(2θ)
Evaluate the power
r=±44csc2(2θ)
Write the expression as a product where the root of one of the factors can be evaluated
r=±42csc2(2θ)
Solution
r=42csc2(2θ)r=−42csc2(2θ)
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−xy
Calculate
9x24y2=36
Simplify the expression
36x2y2=36
Take the derivative of both sides
dxd(36x2y2)=dxd(36)
Calculate the derivative
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Evaluate
dxd(36x2y2)
Use differentiation rules
dxd(36x2)×y2+36x2×dxd(y2)
Evaluate the derivative
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Evaluate
dxd(36x2)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
36×dxd(x2)
Use dxdxn=nxn−1 to find derivative
36×2x
Multiply the terms
72x
72xy2+36x2×dxd(y2)
Evaluate the derivative
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Evaluate
dxd(y2)
Use differentiation rules
dyd(y2)×dxdy
Use dxdxn=nxn−1 to find derivative
2ydxdy
72xy2+72x2ydxdy
72xy2+72x2ydxdy=dxd(36)
Calculate the derivative
72xy2+72x2ydxdy=0
Move the expression to the right-hand side and change its sign
72x2ydxdy=0−72xy2
Removing 0 doesn't change the value,so remove it from the expression
72x2ydxdy=−72xy2
Divide both sides
72x2y72x2ydxdy=72x2y−72xy2
Divide the numbers
dxdy=72x2y−72xy2
Solution
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Evaluate
72x2y−72xy2
Cancel out the common factor 72
x2y−xy2
Reduce the fraction
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Evaluate
x2x
Use the product rule aman=an−m to simplify the expression
x2−11
Subtract the terms
x11
Simplify
x1
xy−y2
Reduce the fraction
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Evaluate
yy2
Use the product rule aman=an−m to simplify the expression
y2−1
Subtract the terms
y1
Simplify
y
x−y
Use b−a=−ba=−ba to rewrite the fraction
−xy
dxdy=−xy
Show Solution

Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=x22y
Calculate
9x24y2=36
Simplify the expression
36x2y2=36
Take the derivative of both sides
dxd(36x2y2)=dxd(36)
Calculate the derivative
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Evaluate
dxd(36x2y2)
Use differentiation rules
dxd(36x2)×y2+36x2×dxd(y2)
Evaluate the derivative
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Evaluate
dxd(36x2)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
36×dxd(x2)
Use dxdxn=nxn−1 to find derivative
36×2x
Multiply the terms
72x
72xy2+36x2×dxd(y2)
Evaluate the derivative
More Steps

Evaluate
dxd(y2)
Use differentiation rules
dyd(y2)×dxdy
Use dxdxn=nxn−1 to find derivative
2ydxdy
72xy2+72x2ydxdy
72xy2+72x2ydxdy=dxd(36)
Calculate the derivative
72xy2+72x2ydxdy=0
Move the expression to the right-hand side and change its sign
72x2ydxdy=0−72xy2
Removing 0 doesn't change the value,so remove it from the expression
72x2ydxdy=−72xy2
Divide both sides
72x2y72x2ydxdy=72x2y−72xy2
Divide the numbers
dxdy=72x2y−72xy2
Divide the numbers
More Steps

Evaluate
72x2y−72xy2
Cancel out the common factor 72
x2y−xy2
Reduce the fraction
More Steps

Evaluate
x2x
Use the product rule aman=an−m to simplify the expression
x2−11
Subtract the terms
x11
Simplify
x1
xy−y2
Reduce the fraction
More Steps

Evaluate
yy2
Use the product rule aman=an−m to simplify the expression
y2−1
Subtract the terms
y1
Simplify
y
x−y
Use b−a=−ba=−ba to rewrite the fraction
−xy
dxdy=−xy
Take the derivative of both sides
dxd(dxdy)=dxd(−xy)
Calculate the derivative
dx2d2y=dxd(−xy)
Use differentiation rules
dx2d2y=−x2dxd(y)×x−y×dxd(x)
Calculate the derivative
More Steps

Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
dx2d2y=−x2dxdy×x−y×dxd(x)
Use dxdxn=nxn−1 to find derivative
dx2d2y=−x2dxdy×x−y×1
Use the commutative property to reorder the terms
dx2d2y=−x2xdxdy−y×1
Any expression multiplied by 1 remains the same
dx2d2y=−x2xdxdy−y
Use equation dxdy=−xy to substitute
dx2d2y=−x2x(−xy)−y
Solution
More Steps

Calculate
−x2x(−xy)−y
Multiply the terms
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Evaluate
x(−xy)
Multiplying or dividing an odd number of negative terms equals a negative
−x×xy
Cancel out the common factor x
−1×y
Multiply the terms
−y
−x2−y−y
Subtract the terms
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Simplify
−y−y
Collect like terms by calculating the sum or difference of their coefficients
(−1−1)y
Subtract the numbers
−2y
−x2−2y
Divide the terms
−(−x22y)
Calculate
x22y
dx2d2y=x22y
Show Solution
