Let P(a1,b1) and Q(a2,b2) be two distinct points on a circle with center C(2,3). Let O be the origin and OC be perpendicular to both CP and CQ. If the area of the triangle OCP is 235, then a12+a22+b12+b22 is equal to __________
Held on 30 Jan 2023 · Verified 6 Jul 2026.
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Let the image of parabola $x^{2}=4 y$, in the line $x-y=1$ be $(y+a)^{2}=b(x-c)$, $a, b, c \in \mathrm{~N}$. Then $a+b+c$ is equal to
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Let a point $A$ lie between the parallel lines $L_{1}$ and $L_{2}$ such that its distances from $L_{1}$ and $L_{2}$ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle $A B C$, where the points $B$ and C lie on the lines $\mathrm{L}_{1}$ and $\mathrm{L}_{2}$, respectively, is :
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