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JEE Previous Year Question

$The value of ' k' so that the line y = 2 x + k may touch the ellipse 3 x^{2} + 5 y^{2} = 15 is$

Topic: JEE PYQ

Answer: A. Full step-by-step solution below.

A $\pm 23$
B $\pm 13$
C $\pm 33$
D $\pm 32$

Correct answer: A

Solution

(a) Condition of tangency is (c^{2} = a^{2} m^{2} + b^{2})) For \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 and y = mx + c is tangent. Here, \frac{x ^{2}}{5} + \frac{y ^{2}}{3} = 1 and y = 2 x + k is a tangent \Rightarrow k^{2} = 5 \times 4 + 3 \Rightarrow k^{2} = 23 \Rightarrow k = \pm 23

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