Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2003MathematicsParabola

The equation of the parabola with focus (0,0) and directrix x+y=4 is

Options

  1. Ax^2+y^2-2 x y+8 x+8 y-16=0
  2. Bx^2+y^2-2 x y+8 x+8 y=0
  3. Cx^2+y^2+8 x+8 y-16=0
  4. Dx^2-y^2+8 x+8 y-16=0

Correct answer

A. x^2+y^2-2 x y+8 x+8 y-16=0

Step-by-step solution

Given focus of parabola is S(0,0) . Equation of directrix is x+y=4 Let P(x, y) be any point on the parabola. Now, S P^2=P M^2 (x-0)^2+(y-0)^2= [ x+y-4 1+1 ]^2 x^2+y^2= (x+y-4)^2 2 2 x^2+2 y^2=x^2+y^2+16+2 x y-8 x-8 y x^2+y^2-2 x y+8 x+8 y-16=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