Question

Two lines through $(2,3)$ from which the circle $x^2+y^2=25$ intercepts chords of length 8 units have equations

• A. $2x+3y=13,x+5y=17$
• B. $y=3,12x+5y=39$
• C. $x=2,9x-11y=51$
• D. none of these

Answer 1

Answer: (B)

Let slope of required line is $m$
$y-3=m(x-2)$
$\Rightarrow mx-y+(3-2m)=0$

length of $\perp$ from origin
$=3$
$\Rightarrow 9+4m^2-12m=9+9m^2$
$\Rightarrow 5m^2+12m=0\Rightarrow m=0,-12/5$
Hence lines are $y-3=0\Rightarrow y=3$
and
$y-3=-\frac{12}{5}(x-2)\Rightarrow 5y-15=-12x+24$
$\Rightarrow 12x+5y=39$