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: The value of r is

Quantrex Academy · Accepted Answer

Correct answer: D. t 2 - 1 t

Slope (QR) = slope (PK) 2 a t - 0 a t 2 - 2 a = - 2 a t - 2 a r a t 2 - a r 2 &#160; &#8658; &#160; &#160; t t 2 - 2 = - 1 t + r 1 t 2 - r 2 &#160; &#160; &#8658; &#160; &#160; &#160; r = t 2 - 1 t

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: The value of r is

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