Question

The equation to two circles which touch the Y-axis at $(0, 3)$ and make an intercept of $8$ units on X-axis are

• A. $x^2 + y^2 \pm 6x -10y + 9 = 0$
• B. $x^2 + y^2 \pm 10x - 6y + 9 = 0$
• C. $x^2 + y^2 + 10x \pm 6y + 9 = 0$
• D. $x^2 + y^2 -8x \pm 10y + 9 = 0$

Answer 1

Answer: (B)

$x^2 + y^2 \pm 10x - 6y + 9 = 0$

Answer 2

Given, equation of circle touch the $y$-axis at $(0, 3)$. So, from figure $r = \sqrt{3^2 + 4^2} = 5$ The point $( 0, 3)$ and radius 5 satisfies the equation $x^2 + y^2 \pm 10 x - 6 y + 9 = 0$ Hence, it is the required equation of circle