If xcos⁡α$$+ysin$$⁡α$$=4$$ is tangent to $$x225+y29=1$$ , then the value of α is

Correct option is 1tan−1⁡(3/7)

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$If x \cos α + y \sin α = 4 is tangent to \frac{x^{2}}{25} + \frac{y^{2}}{9} = 1, then the value of α is$

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detailed solution

Correct option is A

xcos⁡α+ysin⁡α=4∴ y=(−cot⁡α)x+4cosec⁡α∴ m=−cot⁡α,c=4cosec⁡α,a2=25,b2=9 Now c2=a2m2+b2∴ 16cosec2⁡α=25cot2⁡α+9∴ 161+cot2⁡α=25cot2⁡α+9∴ 7=9cot2⁡α⇒cot⁡α=73⇒tan⁡α=37∴ α=tan−1⁡(3/7)

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If xcos⁡α+ysin⁡α=4 is tangent to x225+y29=1 , then the value of α is

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$If x \cos α + y \sin α = 4 is tangent to \frac{x^{2}}{25} + \frac{y^{2}}{9} = 1, then the value of α is$