Question

If a circle pass through (4, 0) and (0, 2) and center at y-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 in a national level competition.

I'd like to ask this question from Conic Sections in chapter Conic Sections of Mathematics – Class 11

Answer 1

The correct answer is (c) 5 units

The best explanation: Equation of circle with center at y-axis (0, b) and radius r units is

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

=>(4)^2+(-b)^2=r^2

And (0)^2+(2-b)^2=r^2

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

So, r^2=4^2+3^2=5^2 => r=5 units.