Question

If a circle pass through (2, 0) and (0, 4) and center at x-axis then find the radius of the circle.

(a) 25 units

(b) 20 units

(c) 5 units

(d) 10 units

I have been asked this question during an interview.

Question is taken from Conic Sections in division Conic Sections of Mathematics – Class 11

Answer 1

Right choice is (c) 5 units

Explanation: Equation of circle with center at x-axis (a, 0) and radius r units is

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

=>(2-a)^2+(0)^2=r^2

And (0-a)^2+(4)^2=r^2

=>(a-2)^2=a^2+4^2 => (-2)(2a-2) =16 => a-1=-4 => a=-3

So, r^2 = (2+3)^2=5^2

r=5 units.