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

If the tangent drawn to the parabola y^2=4 x at (t^2, 2 t ) is the normal to the ellipse 4 x^2+5 y^2=20 at ( 5 , 2 ) , then

Options

  1. A5 t^4+4 t^2=1
  2. B5 t^4 + 100 t^2 =1
  3. Ct=
  4. D=t+1

Correct answer

A. 5 t^4+4 t^2=1

Step-by-step solution

Given, tangent to parabola y^2=4 x at (t^2, 2 t ) is y 2 t=2 (x+t^2 ) y t=x+t^2 Normal to the ellipse 4 x^2+5 y^2=20 or x^2 5 + y^2 4 =1 at ( 5 , 2 ) Slope of normal =5 y / 4 x= 5 2 Equation of line is y-2 = 5 2 (x- 5 ) By comparing Eqs. (i) and (ii), we get t=- 2 aligned 1 t & = 5 2 & = 2 5 t aligned From Eqs. (iii) and (iv), we get -2 t= 2 4+5 t^2 On squaring both sides, we get t^2 (4+5 t^2 )=1 5 t^4+4 t^2=1

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