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NVAMediumJEE Main 2023 · 11 April, Shift 2Conic Sections (Parabola, Ellipse, Hyperbola)

Mathematics Question from JEE Main 2023 · 11 April, Shift 2

Let the tangent to the parabola y2=12xy^2 = 12x at the point (3,α)(3, \alpha) be perpendicular to the line 2x+2y=32x + 2y = 3. Then the square of the distance of the point (6,−4)(6, -4) from the normal to the hyperbola α2x2−9y2=9α2\alpha^2 x^2 - 9y^2 = 9\alpha^2 at its point (α−1,α+2)(\alpha - 1, \alpha + 2) is equal to _____.

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