Q5: Determine the graph of the polar equation r = 10/10-7cos theta.

Question

asked Sep 4, 2020 193k views

2 Answers

Benibr · Answer 1 · 2020-09-09T21:05:34+0000

$r=(10)/(10-7\cos\theta)\implies10r-7r\cos\theta=10$

Converting to Cartesian coordinates using

$x=r\cos\theta$

r=√(x^2+y^2)

we have

10√(x^2+y^2)-7x=10

10√(x^2+y^2)=7x+10

100(x^2+y^2)=(7x+10)^2

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

51x^2-140x+100y^2=100

Complete both squares to get

$51\left(x-(70)/(51)\right)^2-(4900)/(51)+100y^2=100$

$51\left(x-(70)/(51)\right)^2+100y^2=(10,000)/(51)$

$(2601)/(10,000)\left(x-(70)/(51)\right)^2+(51)/(100)y^2=1$

This is the equation of an ellipse, so it's either A or C.

The ellipse is centered at
$\left((70)/(51),0\right)\approx(1.37,0)$ , so it falls to the right of the vertical axis, which means the answer is C.