Related InterviewSolutions

• Let L be the point (t, 2) and M be a point on the y-axis such that the slope of LM is −t. Then, the locus of the midpoint of LM is a parabola whose latus rectum is(a)  2(b)   1/2(c)   4(d)  1/4
• In general, three normals can be drawn through a point in the plane of a parabola to the curve.
• Show that the chords of contacts of points on the line 2x - 3y + 4 = 0 with respect to the parabola y2 = 4ax pass through a fixed point.
• Find the coordinates of the point whose chord of contact with respect to the parabola y2 + 4x is 2x - 7y + 2 = 0
• If P is a point on the line x + 4a = 0 and QR is the chord of contact of P with respect to y2 = 4ax, then ∠QOR (where O is the vertex) is equal to (A)  45°(B)  60°(C)  30°(D)  90°
• Locus of the point of intersection of the tangents to the parabola y2 = 4ax which include 60° angle is(A)   y2 = 4ax + 3(x + a)2(B)   y2 - 4ax = 2(x + a)2(C)   y2 - 4ax = (x + a)2(D)   y2 - 4ax = 3(x + a)3
• Find the distance between foci of the ellipse \(\rm {x^2\over100}+{y^2\over64} = 1\).1. 22. 33. 44. 12
• Passage: For the parabola y2 = 4ax, the vertex is (0, 0), the focus is (a, 0) and the directrix is x + a = 0. Answer the following three questions.(i) The vertex of the parabola (y - 1)2 = 2(x - 1) is (A)  (1,0)(B)  (2,0) (C)  (1,1)(D)  (0,1)(ii)  Focus of the parabola y2 = 4(x - 1) is(A)  (1, 0)(B)  (2, 0)(C)  (1, 1)(D)  (2, 2)(iii)  The directrix of the parabola (y - 2)2 = 4(x - 1)(A)   x = 1(B)   x = -1(C)   x = 2 (D)  x =  0
• Equation of the normal at t istx + y = 2at + at3
• Find the director circle of the parabola x2 + 2y = 4x - 3 .