Question

The length of intercept on $y-axis$, by a circle whose diameter is the line joining the points $(-4,3)$ and $(12,-1)$ is

• A. $3\sqrt{2}$
• B. $\sqrt{13}$
• C. $4\sqrt{13}$
• D. $noneofthese$

Answer 1

Answer: (C)

$4\sqrt{13}$

Equation of circle=

$(x+4)(x-12)+(y-3)(y+1)=0$

$\therefore x^2-8x-48+y^2-2y-3=0$

$\therefore x^2+y^2-8x-2y-51=0$

Now For intercept

Put $x=0$

$y^2-2y-51=0$

$y=2+\sqrt{4+204}$

$\therefore y=\pm \sqrt{52}$

length of intercept $=1+\sqrt{52}-1+\sqrt{12}$

$=2\sqrt{52}$

$=4\sqrt{13}$