The locus of point of intersection of two tangents to the parabola y 2 = 4 x such that their chord of contact subtends a right angle at the vertex is

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Chord of contact of ( t 1 ​ t 2 ​ , t 1 ​ + t 2 ​ ) with respect to y 2 = 4 x is ( t 1 ​ + t 1 ​ ) y = 2 ( x + t 1 ​ t 2 ​ ) ​ ⇒ 2 t 1 ​ t 2 ​ ( t 1 ​ + t 2 ​ ) y − 2 x ​ = 1 = y 2 = 4 x .1 ⇒ t 1 ​ t 2 ​ + 4 = 0 ⇒ t 1 ​ t 2 ​ = − 4 ​ x = − 4 ⇒ x + 4 = 0 ​

Mathematics - Parabola Question with Solution | TestHub

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