Questions
If the line intersects the curve at P and Q such that the circle with PQ as a diameter passes through the origin, then
a
n2(a+b)
b
n2(a+b)2
c
n2a2−b2
d
n2a2+b2
detailed solution
Correct option is A
It is given that the circle with PQ as a diameter passes through the origin. This means that symbol ∠POQ=90∘ i.e. the lines joining the origin to the points of intersection of ax2+2hxy+by2=1 and 1x+my+n=0 are at right angle.The combined equation of OP and OQ is given byax2+2hxy+by2=1x+my−n2This represents a pair of perpendicular lines.∴ Coeff. of x2+ Coeff. of y2=0⇒ an2−l2+bn2−m2=0⇒l2+m2=(a+b)n2Talk to our academic expert!
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