Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced2012MathematicsParabolaActual

Let S be the focus of the parabola y²=8 x and let P Q be the common chord of the circle x²+y²-2 x-4 y=0 and the given parabola. The area of the triangle P Q S is

Correct answer

4

Step-by-step solution

Given parabola y²=8 x and circle x²+y²-2 x-4 y=0 pass through the origin One end of common chord PQ is origin. Say P (0,0) Let Q be the point (2 t², 4 t ) , then it will satisfy the equation of circle. 4 t⁴+16 t²-4 t²-16 t=0 t⁴+3 t²-4 t=0 t (t³+3 t-4 )=0 t(t-1) (t²+t-4 )=0 t=0 or 1 For t=0 , we get point P , therefore t=1 gives point Q as (2,4) . We also observe here that P (0,0) and Q (2,4) are end points of diameter of the given circle and focus of the parabola is the point S(2,0) . area ( PQS )= 1 2 P S Q S= 1 2

Practice Parabola on Quantrex Academy →

More from Parabola

Let T be the tangent to the parabola y^2 = 16x at the point (64, 32) . Let L be the tangent to the same parabola at another point (x₁, y₁) on the parabola. If L and T are perpendic 2026Let O be the vertex of the parabola y^2=4x and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C, then the len 2026Let chord PQ of length 3 13 of the parabola y^2 = 12x be such that the ordinates of points P and Q are in the ratio 1:2 . If the chord PQ subtends an angle at the focus of the para 2026Let the point P be the vertex of the parabola y = x^2 - 6x + 12 . If a line passing through the point P intersects the circle x^2 + y^2 - 2x - 4y + 3 = 0 at the points R and S , th 2026Let the directrix of the parabola P: y^2 = 8x , cut x -axis at the point A . Let B( , ) , > 1 , be a point on P such that the slope of AB is 3/5 . If BC is a focal chord of P , the 2026Let A,B and C be the vertices of a variable right angled triangle inscribed in the parabola y^2=16x . Let the vertex B containing the right angle be (4,8) and the locus of the cent 2026Consider the parabola P : y^2 = 4kx and the ellipse E : x^2 a^2 + y^2 b^2 = 1 . Let the line segment joining the points of intersection of P and E , be their latus rectums. If the 2026Let the parabola y = x^2 + px + q passing through the point (1, -1) be such that the distance between its vertex and the x -axis is minimum. Then the value of p^2 + q^2 is: 2026 Full Parabola list All JEE Advanced PYQs