How do you convert $r = 10/(4 - 7cos(theta))$ to rectangular form?

Question

4447 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-06T18:04:35

$33x^2 -16y^2+140x+100=0$

rectangular and polar form are related as follows:

$x= r cos theta$ and $y= rsin theta$ , so $r^2= x^2 +y^2$

Accordingly, the given expression can be reworked as follows:

$4r -7rcos theta=10$

$4r= 10+7x$ Square both sides,

$16r^2= (10+7x)^2$

$16x^2+16y^2= 100+140x +49x^2$

$33x^2 -16y^2+140x+100=0$

How do you convert r = 10/(4 - 7cos(theta))r = 10/(4 - 7cos(theta)) to rectangular form?