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Q.
The parabola $y=x^2-9$ and $y=k x^2$ intersect each other at the points $A$ and $B$. If the length $A B$ is equal to 10 units then the value of $k$ is equal to
Conic Sections
Solution:
$ x ^2-9= kx ^2 $
$x ^2( k -1)+0 . x +9=0 $
$x _1+ x _2=0 \& x _1 x _2=\frac{9}{ k -1} $
now $\left| x _1- x _2\right|=10=\sqrt{\left( x _1+ x _2\right)^2-4 x _1 x _2}$
$\ 100=\frac{36}{1- k }$
$100-100 k =36 \Rightarrow k =\frac{64}{100}=\frac{16}{25}$
