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

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)