Let m₁, m₂ be the slopes of two adjacent sides of a square of side a such that a²+11 a+3(m₁²+m₂²)=220. If one vertex of the square is (10(cos α- sin α), 10(sin α+ cos α)), where α (0, (π)/2) and the equation of one diagonal is (cos α- sin α) x+(sin α+ cos α) y=10, then 72(sin ⁴ α+ cos ⁴ α)+a²-3 a+13 is equal to:

Coordinate Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 29 Jul, Evening shift · Q5619

JEE Main 202229 Jul, Evening shiftMathematicsHardCoordinate Geometry478× since 2002

Let

m_{1}, m_{2}

be the slopes of two adjacent sides of a square of side a such that

a^{2}+11 a+3\left(m_{1}^{2}+m_{2}^{2}\right)=220

. If one vertex of the square is

(10(\cos \alpha-\sin \alpha), 10(\sin \alpha+\cos \alpha))

, where

\alpha \in\left(0, \frac{\pi}{2}\right)

and the equation of one diagonal is

(\cos \alpha-\sin \alpha) x+(\sin \alpha+\cos \alpha) y=10

, then

72\left(\sin ^{4} \alpha+\cos ^{4} \alpha\right)+a^{2}-3 a+13

is equal to :