Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20244 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
4 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Parabola

JEE Main 2024 · 4 April · Morning Shift · Mathematics · Parabola

Let the length of the focal chord PQ of the parabola y^2=12 x be 15...

Let the length of the focal chord PQ of the parabola y2=12xy^2=12 x be 15 units. If the distance of PQ\mathrm{PQ} from the origin is p\mathrm{p}, then 10p210 \mathrm{p}^2 is equal to _______

Correct answer

0

Step-by-step solution

 length of focal chord =4acosec⁡2θ=1512cosec⁡2θ=15sin⁡2θ=45tan⁡2θ=4tan⁡θ=2 equation y−0x−3=2y=2x−62x−y−6=0P=6510p2=10⋅365=72\begin{aligned} & \text{ length of focal chord }=4 a \operatorname{cosec}^2 \theta=15 \\ & 12 \operatorname{cosec}^2 \theta=15 \\ & \sin ^2 \theta=\frac{4}{5} \\ & \tan ^2 \theta=4 \\ & \tan \theta=2 \\ & \text{ equation } \frac{y-0}{x-3}=2 \\ & y=2 x-6 \\ & 2 x-y-6=0 \\ & P=\frac{6}{\sqrt{5}} \\ & 10 p^2=10 \cdot \frac{36}{5}=72\end{aligned}
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… JEE Advanced 2026Let O be the vertex of the parabola y^2=4x and its chords OP and OQ are perpendicular to… JEE Main 2026Let chord PQ of length 3 13 of the parabola y^2 = 12x be such that the ordinates of… JEE Main 2026Let the point P be the vertex of the parabola y = x^2 - 6x + 12 . If a line passing… JEE Main 2026Let the directrix of the parabola P: y^2 = 8x , cut x -axis at the point A . Let B(α, β)… JEE Main 2026Let A,B and C be the vertices of a variable right angled triangle inscribed in the… JEE Main 2026Consider the parabola P : y^2 = 4kx and the ellipse E : (x^2)/(a^2) + (y^2)/(b^2) = 1 .… JEE Main 2026Let the parabola y = x^2 + px + q passing through the point (1, -1) be such that the… JEE Main 2026Let A be the focus of the parabola y^ 2 =8 x . Let the line y=m x+c intersect the… JEE Main 2026Let the image of parabola x^ 2 =4 y , in the line x-y=1 be (y+a)^ 2 =b(x-c) , a, b, c ∈… JEE Main 2026An equilateral triangle OAB is inscribed in the parabola y^ 2 =4 x with the vertex O at… JEE Main 2026Let the locus of the mid-point of the chord through the origin O of the parabola y^ 2 =4… JEE Main 2026If the chord joining the points P_ 1 (x_ 1 , y_ 1 ) and P_ 2 (x_ 2 , y_ 2 ) on the… JEE Main 2026Let y^ 2 =12 x be the parabola with its vertex at O. Let P be a point on the parabola and… JEE Main 2026Let one end of a focal chord of the parabola y^ 2 =16 x be (16,16) . If P(α, β) divides… JEE Main 2026Let O be the vertex of the parabola x^ 2 =4 y and Q be any point on it. Let the locus of… JEE Main 2026 Full Parabola list Parabola JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs