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If (-2,5) and (3,7) are the points of intersection of the tangent and normal at a point on a parabola \mathrm{y^{2}=4ax} with the axis of the parabola ,then the focal distance of that point is

Option: 1

\frac{\sqrt29}{2}


Option: 2

\frac{5}{2}


Option: 3

\sqrt29


Option: 4

\frac{2}{5}


Answers (1)

best_answer

For parabola \mathrm{y^2=4 a x}, tangent and normal at point \mathrm{P\left(a t^2, 2 a t\right)} meets x-axis at \mathrm{T\left(-a t^2, 0\right)\: and \: N\left(2 a+a t^2, 0\right)}Thus, focus \mathrm{S} is the mid-point of \mathrm{TN}


Also, \mathrm{S P=S T=S N=a+a t^2}

\mathrm{ \therefore S P=T N / 2 }

For given data, \mathrm{ T N=\sqrt{29} }

\mathrm{ \therefore S P=\frac{\sqrt{29}}{2} }

Hence option 1 is correct.

Posted by

Kuldeep Maurya

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