Question

Convert the rectangular equation below to a polar equation. x² - 7x + y²=0

Answer 1

Answer 2

X^2-7x+y^2=0 X=rcos theta and y=rsin theta r^2cos^2 theta -7rcos theta+r^2sin^2 theta =0 r^2cos^2 theta + r^2sin^2 theta =7rcos theta r^2 (cos^2 theta + sin^2 theta)=7rcos 7rcos theta r^2 (1)=7rcos theta r=7cos theta

Answer 3

SOLUTION :

x^2  - 7x + y^2 = 0

To convert to polar coordinates (r, ?) :

we, use the following relationships :

x = r cos ? and y = r sin ?

So,

Given equation becomes :

(r cos ?)^2 - 7(r cos ?) + (r sin ?)^2 = 0

=> (r cos ?)^2 + (r sin ?)^2  -  7(r cos ?)  = 0

=> r^2  - 7r cos ? = 0

=> r - 7 cos ? = 0

=> r = 7 cos ? (ANSWER)