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.
Create a free account to view solution
View Solution FreeMore Parabola Questions
Let PQ be a double ordinate of the parabola, y2 = − 4x, where P lies in the second quadrant. If R divides PQ in th...A parabola passes through (1, 2) and (3, 4). The tangents drawn at these points intersect at (-6, 8), then the slope of ...From the point (4, 6) a pair of tangent lines are drawn to the parabola, y2 = 8x. The area of the triangle formed by the...Point P lies on y2 = 4ax & N is foot of perpendicular from P on its axis. A straight line is drawn parallel to the axis ...If the chord joining the points $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$ on the parabola $y^2 = 12x$ subtends a right angle a...