Question

What is the equation of a circle with radius 2 and center (3, 1)? (x - 3)2 – (y - 1)2 = 4 O (c - 3)2 + (y - 1)2 = 4 (x ) O (x + 3)2 + (y + 1)2 = 4 (x - 3)² + (y - 1)2 = 2

Answer 1

Given the radius of a circle as r = 2 and centre = (3,1)

We want to find the equation

Solution

First, the equation of a circle centre (a,b) and radius r is given by

`(x-a)^2+(y-b)^2=r^2`

From the question

`\begin{gathered} a=3 \\ b=1 \\ r=2 \end{gathered}`

We put the parameters into the equation ans simplify

`\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ (x-3)^2+(y-1)^2=2^2 \\ (x-3)^2+(y-1)^2=4 \end{gathered}`

Therefore the correct option is Option B