Highly selective Backlog Qs for JEE MainMathematicsParabola

Let the focus S of the parabola y 2 =8 x lies on the focal chord P Q of the same parabola. If P S = 6 , then the square of the slope of the chord P Q is

Options

A2 5
B4 5
C5 4
D9 4

Correct answer

B. 4 5

Step-by-step solution

We know that, P S , 4 , S Q are in H . P . ⇒ 1 6 , 1 4 , 1 S Q are in A . P . ⇒ 1 S Q = 2 4 - 1 6 = 1 3 ⇒ S Q = 3 ⇒ P Q = 6 + 3 = 9 = 4 c o s e c 2 θ (where, tan ⁡ θ is the slope of P Q ) ⇒ 1 + cot 2 ⁡ θ = 9 4 ⇒ cot 2 ⁡ θ = 5 4 ⇒ tan 2 ⁡ θ = 4 5

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 2026 Let 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 2026 Let 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 2026 Let 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 2026 Let 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 2026 Let 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 2026 Consider 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 2026 Let 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 Highly selective Backlog Qs for JEE Main PYQs