Q.

Through a point A on the x-axis, a straight line is drawn parallel to the y-axis so as to meet the pair of straight lines ax2+2hxy+by2=0 at B and C. If AB=BC, then

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a

h2=4ab

b

8h2=9ab

c

9h2=8ab

d

4h2=ab

answer is B.

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Detailed Solution

Given AB =BC.Also,m1+m2=2hb and m1m2=abtan θ=ABOA=m1and m2=tan α=2ABOA=2m1∴ m2m1=2or m2+m1m2−m1=2+12−1=3or −2h/b(4h2/b2)−(4a/b)=3or 4h2b2.b24(h2−ab)=9or 9h2−9ab=h2 or 8h2=9ab
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Through a point A on the x-axis, a straight line is drawn parallel to the y-axis so as to meet the pair of straight lines ax2+2hxy+by2=0 at B and C. If AB=BC, then