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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 t1t2)


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(t1t2)=a(t21t22)

=a(t1t2)(t1+t2)

y=a(t1+t2)

(since t1t20)

=2at1+2at22

= AM of x coordinates

Solving (3)&(1)

x=t1yat21

=t1.a.(t1+t2)at21

=at21+at1t2at21

=at1t2

at21×at22

=GM of y coordinates

Hence option (b) is correct


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