Consider a circle C₁: x²+y²-4 x-2 y=α-5. Let its mirror image in the line y=2 x+1 be another circle C₂: 5 x²+5 y²-10 f x-10 g y+36=0. Let r be the radius of C₂. Then α+r is equal to _ _ _ _ _.

Coordinate Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 8 Apr, Morning shift · Q29

JEE Main 20238 Apr, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

Consider a circle

C_{1}: x^{2}+y^{2}-4 x-2 y=\alpha-5

. Let its mirror image in the line

y=2 x+1

be another circle

C_{2}: 5 x^{2}+5 y^{2}-10 f x-10 g y+36=0

. Let

r

be the radius of

C_{2}

. Then

\alpha+r

is equal to _________.

Your answerType your answer. Integers and decimals are accepted.