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  4. Two lines through (2,3) from which the circle x2+y2=25 intercepts chords of length 8 units have equations

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

Conic Sections

Solution:

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