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Question

The locus of point of intersection of the lines
txayb+t=0, xa+tyb1=0 is (t is a parameter and ab)

A
parabola
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B
circle
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C
pair of straight lines
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D
ellipse
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Solution

The correct option is D ellipse
txayb+t=0 (1)
xa+tyb1=0 (2)
From equations (1) and (2), the point of intersetion is
(h,k)(a(1t21+t2),2bt1+t2)ha=1t21+t2,kb=2t1+t2h2a2+k2b2=(t21)2+4t2(1+t2)2h2a2+k2b2=(t2+1)2(1+t2)2=1

Hence locus will be
x2a2+y2b2=1
Which is an ellipse.

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