Let the lines y + 2x = √(11) + 7 7 and 2y + x = 2√(11) + 6 7 be normal to a circle C:(x - h)² + (y - k)² = r². If the line √(11) y - 3x = (5√(77))/3 + 11 is tangent to the circle C, then the value of (5h - 8k)² + 5r² is equal to _ _ _ _ _.

Coordinate Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 28 Jun, Morning shift · Q34

JEE Main 202228 Jun, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

Let the lines

y + 2x = \sqrt {11} + 7\sqrt 7

and

2y + x = 2\sqrt {11} + 6\sqrt 7

be normal to a circle

C:{(x - h)^2} + {(y - k)^2} = {r^2}

. If the line

\sqrt {11} y - 3x = {{5\sqrt {77} } \over 3} + 11

is tangent to the circle C, then the value of

{(5h - 8k)^2} + 5{r^2}

is equal to __________.

Your answerType your answer. Integers and decimals are accepted.