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Question

The coordinate axes are rotated about the origin (0,0) in counter clockwise direction through an angle of 600. lf p and q are intercepts made on new axes by a straight line whose equation referred to the original axes is x+y=1, then 1p2+1q2=

A
2
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B
4
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C
6
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D
8
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Solution

The correct option is A 2

When axes are rotated through 600, co-ordinates are

x=xcosθysinθ=x2y32

y=xsinθycosθ=x32y2

x+y=1x2y32+x32+y2=1

x(1+3)2+y(13)2=1

p=21+3;q=213

1p2=1+3+234;1q2=1+3234

1p2+1q2=4+44=2


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