Question

The graph of $r=10\cos \left(\Theta \right)$, where $r$ and $\Theta$ are the polar coordinates, is

• A. A circle
• B. An ellipse
• C. A horizontal line
• D. A hyperbola
• E. A vertical line

Answer 1

The correct option is A A circle

Given $r=10cos\left(\Theta \right)$

Multiply with $r$ on both sides

$\Rightarrow r^2=10rcos\left(\Theta \right)$

If we convert it into Cartesian coordinate plane , we have $r^2=x^2+y^2$ and $rcos\left(\Theta \right)=x$

$\Rightarrow x^2+y^2=10x$

$\Rightarrow {(x-5)}^2+y^2=25$

Therefore the graph represents a circle