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Class XI Maths Conic Section 1 - Parabola

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Question 1

The equation of normal in terms of slope m to the parabola (y – 2)² = 4 (x – 3) is -

Question 2

Let the line lx + my = 1 cut the parabola y² = 4ax in the points A and B. Normals at A and B meet at point C. Normal from C other than these two meet the parabola at D, then the coordinate of D are

Question 3

If the normal at three points (ap², 2ap), (aq², 2aq) and (ar², 2ar) are concurrent then the common root of equations px² + qx + r = 0 and a(b – c) x² + b(c – a) x + c(a – b) = 0 is

Question 4

If a ≠ 0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y²=4ax and x²=4ay, then

Question 5

The locus of the vertices of the family of parabolas is

Question 6

A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at

Question 7

If t₁ and t₂ be the ends of a focal chord of the parabola y² = 4ax, then the equation t₁x² + ax + t₂ = 0 has

Question 8

The length of a focal chord of the parabola y² = 4ax at a distance b from the vertex is c. Then

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