Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET2011MathematicsParabola

The equations of the normals at the ends of the latusrectum of the parabola y²=4 a x are given by

Options

  1. Ax²-y²-6 a x+9 a²=0
  2. Bx²-y²-6 a x-6 a y+9 a²=0
  3. Cx²-y²-6 a y+9 a²=0
  4. DNone of the above

Correct answer

A. x²-y²-6 a x+9 a²=0

Step-by-step solution

The coordinates of the ends of the latusrectum of the parabola y²=4 a x are (a, 2 a) respectively. The equation of the normal at (a, 2 a) to y²=4 a x is y-2 a= -2 a 2 a (x-a) or x+y-3 a=0 Similarly, the equation of the normal (a,-2 a) is x-y-3 a=0 The combined equation is x²-y²-6 a x+9 a²=0

Practice Parabola on Quantrex Academy →

More from Parabola

A parabola has its focus on the positive X-axis and the Y-axis as its directrix. If P( , 4) is a point on this parabola such that the tangent to the parabola at point P passes thro 2026The distance of the focus of the parabola y^2 = 16x from its directrix is... 2026The area of the triangle formed by the lines joining the vertex of the parabola x^2 = 48y to the ends of its latus rectum, is ..... 2026A point on the parabola y^2 = 36 5 x at which the ordinate increases at thrice the rate of the abscissa is ..... 2026A circle is drawn with its centre at the focus of the parabola y^2=2 p x such that it touches the directrix of the parabola. Then a point of intersection of the circle and the para 2025If the locus of a point that divides a chord of slope 2 of the parabola y^2=4 x internally in the ratio 1: 2 is a parabola, then its vertex is 2025If x-y-3=0 is a normal drawn through the point (5,2) to the parabola y^2=4 x , then the slope of the other normal that can be drawn through the same point to the parabola y^2=4 x i 2025If the normal chord draw n at the point ( 15 2 , 15 2 ) to the parabola y ^2=15 x subtends an angle at the vertex of the parabola, then 3 + 2 3 - 4 3 = 2025 Full Parabola list All MHT CET PYQs