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

Question

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: The value of r is

TestHub · Accepted Answer

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 ⇒ t t 2 - 2 = - 1 t + r 1 t 2 - r 2 ⇒ r = t 2 - 1 t

Mathematics - Parabola Question with Solution | TestHub

Options:

Doubts & Discussion