Through the vertex ' O ' of parabola y 2 = 4 x , chords OP and OQ are drawn at right angles to one another. Then the locus of middle point of PQ is a parabola with Latus rectum λ , then λ eq

Question

Through the vertex ' O ' of parabola y 2 = 4 x , chords OP and OQ are drawn at right angles to one another. Then the locus of middle point of PQ is a parabola with Latus rectum λ , then λ equals

TestHub · Accepted Answer

h = 2 t 1 2 ​ + t 2 2 ​ ​ k = 2 2 ( t 1 ​ + t 2 ​ ) ​ = t 1 ​ + t 2 ​ also t 1 ​ t 2 ​ = − 4 ⇒ 2 h + ( t 1 ​ + t 2 ​ ) 2 − 2 t 1 ​ t 2 ​ ​ 2 h = k 2 + 8 ​ y 2 = 2 ( x − 4 ) ​ ∴ Latus rectum = 2

Mathematics - Parabola Question with Solution | TestHub

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