JEE Main 2025 (Online) 3rd April Morning Shift | Parabola Question 5 | Mathematics

Let the point P of the focal chord PQ of the parabola $y^2=16 x$ be $(1,-4)$. If the focus of the parabola divides the chord $P Q$ in the ratio $m: n, \operatorname{gcd}(m, n)=1$, then $m^2+n^2$ is equal to :

JEE Main 2025 (Online) 2nd April Morning Shift

MCQ (Single Correct Answer)

-1

Let the focal chord PQ of the parabola $y^2=4 x$ make an angle of $60^{\circ}$ with the positive $x$ axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the $y$-axis at the point $(0, \alpha)$, then $5 \alpha^2$ is equal to:

JEE Main 2025 (Online) 29th January Morning Shift

MCQ (Single Correct Answer)

-1

Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersect at the points A and B, then (AB)² is equal to :

384

392

192

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