Question

Find the equation of circle whose centre is on y axis with radius 5 and passes through (1,1)

Answer 1

The equation of a circle with centre at (h,k) and radius r is given by

(x-h)^2 + (y-k)^2 = r ^2..(1)

Given radius r = 5,

Since centre is on y-axis, its coordinates can be taken as (0,a). So h = 0, k = a.

Substituting these in (1) we have

x^2 + (y-a)^2 = 5^2. ………….(2)

Given the circle passes through (3, 2)

So 3^2 +(2-a)^2 = 5^2

=> (2-a)^2 = 5^2–3^2

=> (2-a)^2 = 16

=> 2-a = ± 4

=> a = -2 or 6.