Problem 251

Problem 215

Write the equation of the circle with the given center and radius: Center at (1, 2); radius = $\frac{1}{2}$

Solution

when center (x1,y1)and the radius R are given then

the equaiton of circle is

(x – x₁ )²+ (y-y₁ )² = R ²

center is (1,0)

and radius is $\frac{1}{2}$

put all values in above formula

(x-1)²+ (y – 0)²= ( $\frac{1}{2}$ )²

x²+ 1 – 2 x + y²= $\frac{1}{4}$

x²– y²+ 1 – $\frac{1}{4}$ =0

x²– y²– $\frac{3}{4}$ =0

4x ²– 4y ²– 3=0