Question

Convert the rectangular equation x^2 + y^2 - 5y = 0 into a polar equation.

Answer 1

Note that in polar coordinates, $r^2=x^2+y^2$ and $y = r \sin \theta$.  This gives:

$r^2 - 5r \sin \theta$

$r^2 = 5r \sin \theta$

This gives $r=0$ or $r=5 \sin \theta$.

Answer 2

The polar form is r = 5sinθ of the rectangular equation x^2 + y^2 - 5y is equal to zero.

What is the polar equation?

A polar coordinate system is a two-dimensional coordinate system in which a distance from a reference point and an angle from a reference direction identify each point on a plane.

To convert the rectangular form to a polar form

Plug x = rcosθ and y = rsinθ

Here $\rm r =\sqrt{x^2+y^2}$

$\rm x^2 + y^2 - 5y = 0\\\\(rcos\theta)^2+(rsin\theta)^2- 5(rsin\theta) = 0$

After solving, we get:

$\rm r^2cos^2\theta+r^2sin^2\theta- 5(rsin\theta) = 0\\\\\rm rcos^2\theta+rsin^2\theta- 5sin\theta = 0$

r = 5sinθ

Thus, the polar form is r = 5sinθ of the rectangular equation x^2 + y^2 - 5y is equal to zero.

Learn more about the polar form here:

https://brainly.com/question/13640455

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