Find the equations of the circles touching y-axis at (0,3) and making an intercept of 8 units on the x-axis.

Options

A. `x^(2) + y^(2) pm 10 x - 6y + 9 = 0`
B. `x^(2) + y^(2) pm 6x - 10 y + 9 = 0`
C. `x^(2) + y^(2) -8 x pm 10 y + 9 = 0`
D. `x^(2) + y^(2) + 10 x pm 6y + 9 = 0`

Answer

A

Explanation

Given equation of circle touch the Y-axis at(0,3).
In `triangle AOB, r = sqrt(3^(2) + 4^(2)) = 5`

The point (0, 3) and radius 5 satisfies the equation
`x^(2) + y^(2) pm 10x - 6y + 9 = 0.`