ParabolaHard
Question
AB, AC are tangents to a parabola y2 = 4ax, p1 p2 and p3 are the lengths of the perpendiculars from A, B and C respectively on any tangent to the curve, then p2, p1, p3 are in-
Options
A.A.P.
B.G.P.
C.H.P.
D.none of these
Solution
Let B = (at12, 2at1); C = (at22, 2at2)
A = (at1t2, a(t1 + t2))
equation of tangent of y2 = 4ax at (at2, 2at)
ty = x + at2 ... (1)
p1 =
p2 =
p3 =
⇒ p12 = p2 p3. Hence p2, p1, p3 in G. P.
A = (at1t2, a(t1 + t2))
equation of tangent of y2 = 4ax at (at2, 2at)
ty = x + at2 ... (1)
p1 =
p2 =
p3 =
⇒ p12 = p2 p3. Hence p2, p1, p3 in G. P.
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