Q. 2 - Calculus

Question

Fill in the blanks to complete each of the following theorem statements:  

For, the graph of the equation r = 2a cos θ is ..................the whose equation in rectangular coordinates is:.................

Step-by-Step Solution

Answer

The blanks are filled in order as:

1. Circle 

2.${\left(x-a\right)}^2+y^2=a^2$

Step 1. Given information

$r=2a\cos \theta$

Step 2. Convert the polar equation into rectangular form.

$$\begin{gathered} r=2a\cos \theta \\ r=2a\left(\frac{x}{r}\right) \\ {r}^2=2ax \\ {x}^2+y^2=2ax \\ {x}^2-2ax+y^2=0 \\ {x}^2-2ax+a^2+y^2=a^2 \\ {\left(x-a\right)}^2+y^2=a^2 \end{gathered}$$

This is equation of the circle having center at $\left(a,0\right)$.