Paragraph: Let a , r , s , t be nonzero real numbers. Let P ( a t 2 , 2 a t ) , Q , R ( a r 2 , 2 a r ) and S ( a s 2 , 2 a s ) be distinct points on the parabola y 2 = 4 a x . Suppose that PQ is the

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Paragraph: Let a , r , s , t be nonzero real numbers. Let P ( a t 2 , 2 a t ) , Q , R ( a r 2 , 2 a r ) and S ( a s 2 , 2 a s ) be distinct points on the parabola y 2 = 4 a x . Suppose that PQ is the focal chord and lines QR and P K are parallel, where K is the point ( 2 a , 0 ) . Question: If s t = 1 , then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is

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Tangent at P: ty = x + a t 2 o r y = x t + a t Normal at S: y + x t = 2 a t + a t 3 Solving, 2 y = a t + 2 a t + a t 3 y = a t 2 + 1 2 2 t 3

Mathematics - Parabola Question with Solution | TestHub

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