Q. The equation of the circle of radius 5 in the first quadrant which touches $x$-axis and the line $4y = 3x$ is
A) $x^{2} + y^{2} - 24x - y - 25 = 0$
B) $x^{2} + y^{2} - 30x - 10y + 225 = 0$
C) $x^{2} + y^{2} - 16x - 18y + 64 = 0$
D) $x^{2} + y^{2} - 20x - 12y + 144 = 0$
Explanation
(b)
Let the centre of circle be $(g,\ 5)$
$\therefore\ \ \ \frac{3(g) - 4(5)}{\sqrt{3^{2} + 4^{2}}} = 5$ [radius]
$\Rightarrow \ \ \ 3g = 25 + 20\ \ \Rightarrow \ \ g = 15$
$\therefore$ Equation of circle whose centre (15, 5) and radius 5 is
$(x - 15)^{2} + (y - 5)^{2} = 5^{2}$
$\Rightarrow \ \ \ x^{2} - 30x + y^{2} - 10y + 225 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.