Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KVPY2015MathematicsParabola

Suppose OABC is a rectangle in the xy -plane where o is the origin and A , B lie on the parabola y = x ² . Then C must lie on the curve.

Options

  1. Ay=x²+2
  2. By=2 x²+1
  3. Cy=-x²+2
  4. Dy=-2 x²+1

Correct answer

A. y=x²+2

Step-by-step solution

m_ O A m_ O B =-1t₁ t₂=-1t₁+t₂=hK= (t₁+t₂ )²-2 t₁ t₂K=h²+2 y=x²+2

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 KVPY PYQs