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 ______.

विकल्प

• (3, 10)

• (3, 5)

• (2, 3)

• (1, 5)

Answer 1

A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point (3, 10).

Explanation:

Let centre of the circle is C and the circle cuts the y-axis at B and A. Let the mid-point of chord BA be M.

CB = `sqrt(MC^2 + MB^2)`

`sqrt(3^2 + 4^2)` = 5 = radius of circle

∴ Equation of circle is (x – 3)² + (y – 5)² = 5²

(3, 10) satisfies this equation.

Although there will be another circle satisfying the same conditions that will lie below the x-axis having equation (x – 3)² + (y – 5)² = 5².