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  4. If 2 x+3 y=α, x-y=β and k x+15 y=r are 3 concurrent normal of parabola y2=λ x then value of k is

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Q. If $2 x+3 y=\alpha, x-y=\beta$ and $k x+15 y=r$ are $3$ concurrent normal of parabola $y^{2}=\lambda x$ then value of $k$ is

Conic Sections

Solution:

$t_{1}+t_{2}+t_{3}=0$
$\Rightarrow\left(\frac{-2}{3}\right)+1+\left(\frac{-k}{15}\right)=0$
$\Rightarrow \frac{k}{15}=\frac{1}{3} \Rightarrow k=5$