Question

# Tangents drawn at A(at21,2at1) and B (at22,2at2) intersect at (p,q). Then p and q are ____and ____ of corresponding x and y coordinates of A and B respectively (given t1≠t2)

A

GM, HM

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B

GM, AM

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C

AM, GM

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D

AM, HM

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Solution

## The correct option is B GM, AM let's write equation of tangents at the points A nad B. on solving these tangents we get the point of intersection of these lines. Tangent at A t1y=x+at21 .......(1) Tangent at B t2y=x+at22 .......(1) solving (1) and (2) (1)-(2) y(t1−t2)=a(t21−t22) =a(t1−t2)(t1+t2) y=a(t1+t2) (since t1−t2≠0) =2at1+2at22 = AM of x coordinates Solving (3)&(1) x=t1y−at21 =t1.a.(t1+t2)−at21 =at21+at1t2−at21 =at1t2 √at21×at22 =GM of y coordinates Hence option (b) is correct

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