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  • If the tangents and normals at the extremities of a focal chord of a parabola intersect at <img alt="\mathrm{\left(x_1, y_1\right)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7

If the tangents and normals at the extremities of a focal chord of a parabola intersect at \mathrm{\left(x_1, y_1\right)} and \mathrm{\left(x_2, y_2\right)} respectively, then
 

Option: 1

\mathrm{ x_1=x_2}


Option: 2

\mathrm{ x_1=y_2}


Option: 3

\mathrm{ y_1=y_2}


Option: 4

\mathrm{ x_2=y_1}


Answers (1)

best_answer

Meeting point of tangents \mathrm{\left(a t_1 t_2, a\left(t_1+t_2\right)\right) }

Meeting point of normals \mathrm{\left(2 a+a\left(t_1^2+t_2^2+t_1 t_2\right),-a t_1 t_2\left(t_1+t_2\right)\right) }

\mathrm{ y_1=a\left(t_1+t_2\right) ; y_2=-a t_1 t_2\left(t_1+t_2\right)=a\left(t_1+t_2\right) \text { (using } t_1 t_2=-1 \text { ) } }

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avinash.dongre

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