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Class XI Maths Conic Section 2 - Parabola

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Question 1

If two of the three feet of normals drawn from a point to the parabola y² = 4x be (1, 2) and (1, –2) then the third foot is

Question 2

If two tangents drawn from the point (α, β) to the parabola y² = 4x be such that the slope of one tangent is double of the other then

Question 3

If line 3x + y = 8 meets the parabola (y – 2)² = 4(x – 1) at A and B, then the point of intersection of tangents drawn at A and B lies on line

Question 4

Let tangent at P(3, 4) to the parabola (y – 3)² = (x – 2) meets line x = 2 at A and if S be the focus of parabola then ∠SAP is equal to

Question 5

The other extremity of the focal chord of the parabola y² = 8x which is drawn at the point (1/2, 2) is

Question 6

The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is x – y + 1 = 0, is

Question 7

The set of points on the axis of the parabola y² – 2y – 4x + 5 = 0, from which all the three normals to the parabola are real is

Question 8

The points on the axis of the parabola 3 y²– 4y – 6x + 8 =0 from where 3 distinct normals can be drawn is given by

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