Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=0
Evaluate
4410x=4620y
To find the x-intercept,set y=0
4410x=4620×0
Any expression multiplied by 0 equals 0
4410x=0
Solution
x=0
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Solve the equation
Solve for x
Solve for y
x=2122y
Evaluate
4410x=4620y
Divide both sides
44104410x=44104620y
Divide the numbers
x=44104620y
Solution
x=2122y
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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
4410x=4620y
To test if the graph of 4410x=4620y is symmetry with respect to the origin,substitute -x for x and -y for y
4410(−x)=4620(−y)
Evaluate
−4410x=4620(−y)
Evaluate
−4410x=−4620y
Solution
Symmetry with respect to the origin
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Rewrite the equation
Rewrite in polar form
Rewrite in standard form
Rewrite in slope-intercept form
r=0θ=arctan(2221)+kπ,k∈Z
Evaluate
4410x=4620y
Move the expression to the left side
4410x−4620y=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
4410cos(θ)×r−4620sin(θ)×r=0
Factor the expression
(4410cos(θ)−4620sin(θ))r=0
Separate into possible cases
r=04410cos(θ)−4620sin(θ)=0
Solution
More Steps

Evaluate
4410cos(θ)−4620sin(θ)=0
Move the expression to the right side
−4620sin(θ)=0−4410cos(θ)
Subtract the terms
−4620sin(θ)=−4410cos(θ)
Divide both sides
cos(θ)−4620sin(θ)=−4410
Divide the terms
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Evaluate
cos(θ)−4620sin(θ)
Use b−a=−ba=−ba to rewrite the fraction
−cos(θ)4620sin(θ)
Rewrite the expression
−4620cos−1(θ)sin(θ)
Rewrite the expression
−4620tan(θ)
−4620tan(θ)=−4410
Multiply both sides of the equation by −46201
−4620tan(θ)(−46201)=−4410(−46201)
Calculate
tan(θ)=−4410(−46201)
Calculate
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Evaluate
−4410(−46201)
Multiplying or dividing an even number of negative terms equals a positive
4410×46201
Reduce the numbers
21×221
Multiply the numbers
2221
tan(θ)=2221
Use the inverse trigonometric function
θ=arctan(2221)
Add the period of kπ,k∈Z to find all solutions
θ=arctan(2221)+kπ,k∈Z
r=0θ=arctan(2221)+kπ,k∈Z
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Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=2221
Calculate
4410x=4620y
Take the derivative of both sides
dxd(4410x)=dxd(4620y)
Calculate the derivative
More Steps

Evaluate
dxd(4410x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
4410×dxd(x)
Use dxdxn=nxn−1 to find derivative
4410×1
Any expression multiplied by 1 remains the same
4410
4410=dxd(4620y)
Calculate the derivative
More Steps

Evaluate
dxd(4620y)
Use differentiation rules
dyd(4620y)×dxdy
Evaluate the derivative
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Evaluate
dyd(4620y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
4620×dyd(y)
Use dxdxn=nxn−1 to find derivative
4620×1
Any expression multiplied by 1 remains the same
4620
4620dxdy
4410=4620dxdy
Swap the sides of the equation
4620dxdy=4410
Divide both sides
46204620dxdy=46204410
Divide the numbers
dxdy=46204410
Solution
dxdy=2221
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Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=0
Calculate
4410x=4620y
Take the derivative of both sides
dxd(4410x)=dxd(4620y)
Calculate the derivative
More Steps

Evaluate
dxd(4410x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
4410×dxd(x)
Use dxdxn=nxn−1 to find derivative
4410×1
Any expression multiplied by 1 remains the same
4410
4410=dxd(4620y)
Calculate the derivative
More Steps

Evaluate
dxd(4620y)
Use differentiation rules
dyd(4620y)×dxdy
Evaluate the derivative
More Steps

Evaluate
dyd(4620y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
4620×dyd(y)
Use dxdxn=nxn−1 to find derivative
4620×1
Any expression multiplied by 1 remains the same
4620
4620dxdy
4410=4620dxdy
Swap the sides of the equation
4620dxdy=4410
Divide both sides
46204620dxdy=46204410
Divide the numbers
dxdy=46204410
Cancel out the common factor 210
dxdy=2221
Take the derivative of both sides
dxd(dxdy)=dxd(2221)
Calculate the derivative
dx2d2y=dxd(2221)
Solution
dx2d2y=0
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