Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201921 Apr 2019Evening ShiftMathematicsParabolaActual

The normal at a point on the parabola y 2 = 4 x passes through ( 5 , 0 ) . If two more normals to this parabola also pass through ( 5 , 0 ) , then the centroid of the triangle formed by the feet of these three normals is

Options

  1. A1 2 , 1 2
  2. B( 2 , 0 )
  3. C( 5 , 0 )
  4. D( 0 , 2 )

Correct answer

B. ( 2 , 0 )

Step-by-step solution

The given equation of a parabola, y 2 = 4 x The equation of normal at a point P ( 5 , 0 ) y = - t x + 2 t + t 3 0 = - 5 t + 2 t + t 3 3 t = t 3 t 2 = 3 t = ± 3 , 0 Here, a = 1 Co-normal point P a t 1 2 , 2 a t 1 = ( 3 , 2 3 ) Q a t 2 2 , 2 a t 2 = ( 3 , - 2 3 ) R a t 3 2 , 2 a t 3 = ( 0 , 0 ) The centroid is, C = 3 + 3 + 0 3 , 2 3 - 2 3 + 0 3 C = 6 3 , 0 = 2 , 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 AP EAMCET PYQs