13if the tangents at the extremities of a chord PQ of a parabola intersect at T, then the distance of focus of the parabola from the points P,T,Q are in
1. AP
2. HP
3. GP
4. NONE
The line y=3x bisects the angle between pairs of lines ax2 + 2axy + y2 = 0
if a =
1. 3
2. 11
3. 3/11
4. 11/3
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8 Answers
13
392] let the coordinates of P be [at21, 2at1] and
that of Q be [at22,2at2]
now point of intersection of tangents at t1 and t2 is [at1t2,a(t1+t2)] which are the coordinates of T
now focus `S` is [a,0]
SP =√[ (a-at21)2 +4a2t21] =a+at21
SQ=√[ (a-at22)2 +4a2t22] =a+at22
ST =√[(a-at1t2)2+(at1+at2)2]
now u can solve deepanshu
91)let
y = mx
m2 + 2am +a =0
m = tanα , tanβ are 2 sols
and 3 = tan(α +β /2)
ie tan(α +β) =2.3/1-32 =-3/4 = ± tanα - tanβ /1+tanαtanβ
3/4 =| √4a2 - 4a / 1+a |
now solve