Question

How do you convert `8=(3x-y)^2+y-5x` into polar form?

Answer 1

`r^2(3cos theta-sin theta)^2+r(sin theta-5cos theta)-8=0` representing a small-size parabola-

Explanation:

As the second degree terms form a perfect square, the equation

represents a parabola.

The conversion formula is #(x, y) = r(cos theta, sin theta).

Substitutions give the form given in the answer,

It is incredible but true. This equation would reduce to the simple

form

`2a/r=1+cos theta`

referred to the focus as pole ( r = 0 ) and the axis, `rarr` vertex, as

`theta = 0`. Here, ( the focus-vertex distance ) a is the size of the

parabola

graph{(3x-y)^2+y-5x-8=0 [-40, 40, -20, 20]}