Question

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

Answer 1

C

Explanation:

edge

Answer 2

`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.