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Question: If line \(\frac{\sqrt{2}x}{a}\) – \(\frac{\sqrt{2}y}{b}\) = 2 is tangent to \(\frac{x^{2}}{a^{2}}\)+...

If line 2xa\frac{\sqrt{2}x}{a} – 2yb\frac{\sqrt{2}y}{b} = 2 is tangent to x2a2\frac{x^{2}}{a^{2}}+y2b2\frac{y^{2}}{b^{2}}= 1 then eccentric angle of point at which this line is tangent :

A

π4\frac{\pi}{4}

B

3π4\frac{3\pi}{4}

C

5π4\frac{5\pi}{4}

D

7π4\frac{7\pi}{4}

Answer

7π4\frac{7\pi}{4}

Explanation

Solution

Any tangent xcos⁡θa+ysin⁡θb\frac{x\cos\theta}{a} + \frac{y\sin\theta}{b} = 1

compare x2a\frac{x}{\sqrt{2}a} – y2b\frac{y}{\sqrt{2}b} = 1

cos q = 12\frac{1}{\sqrt{2}} & sin q = – 12\frac{1}{\sqrt{2}} Ž q = 7π4\frac{7\pi}{4}