Question

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

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

Answer 1

The correct option is C $4\sqrt{13}$

Equation of circle is $(x-4{)}^2+(y-1{)}^2=r^2$

$r=\sqrt{8^2+2^2}=\sqrt{68}$

$\to x^2+16-8x+y^2+1-2y=68$

$x^2+y^2-8x-2y-51=0$ ....(1)

$y-$ incercept is nothing but

$2\sqrt{f^2-c}=2\sqrt{(-1{)}^2-(-51)}$

Comparing weith eq. of circle $f=1$

from (1) $f=-1=2\sqrt{52}$

$=2\sqrt{4\times 13}$

$=4\sqrt{13}$

Answer C) $4\sqrt{13}$