Paragraph: Let a, r, s, t be nonzero real numbers. Let P (a t², 2 a t ), Q, R (a r², 2 a r ) and S (a s², 2 a s ) be distinct points on the parabola y²=4 a x . Suppose that P Q is the focal chord and lines Q R and P K are parallel, where K

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Paragraph: Let a, r, s, t be nonzero real numbers. Let P (a t², 2 a t ), Q, R (a r², 2 a r ) and S (a s², 2 a s ) be distinct points on the parabola y²=4 a x . Suppose that P Q is the focal chord and lines Q R 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

Quantrex Academy · Accepted Answer

Correct answer: B. a t 2 + 1 2 2 t 3

Tangent at P: ty = x + a t 2 &#160; o r &#160; 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

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