JEE PYQ: Parabola Question 25
Question 25 - 2019 (10 Jan Shift 2)
The length of the chord of the parabola $x^2 = 4y$ having equation $x - \sqrt{2}y + 4\sqrt{2} = 0$ is:
(1) $3\sqrt{2}$
(2) $2\sqrt{11}$
(3) $8\sqrt{2}$
(4) $6\sqrt{3}$
Show Answer
Answer: (4)
Solution
Substituting $x = \sqrt{2}y - 4\sqrt{2}$ in $x^2 = 4y$: $\sqrt{2}x^2 - 4x - 16\sqrt{2} = 0$. $(x_1 - x_2)^2 = (x_1+x_2)^2 - 4x_1 x_2 = 8 + 64 = 72$. Length $= |x_1 - x_2|\sqrt{1 + \frac{1}{2}} = \sqrt{72} \cdot \frac{\sqrt{3}}{\sqrt{2}} = 6\sqrt{3}$.
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