Question

A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point :
(A) (3, 5) (B) (1, 5)
(C) (3, 10) (D) (2, 3)

Answer 1

A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis.

• Let us draw a circle touching (3,0) with random dimensions.

• We need to find the radius of the circle.

• We also need to find the center of the circle.

• We know, Radius perpendicular to the chord of circle bisects it.

• By solving, we get radius as 5 and centre as (3,5).

• With these , equatin of a circle with center (3,5) and radius 5 is written.

• By plugging the options in our equation,

(3,10) satisfies the equation.

• So, option C is the right answer.