JEE Main 2022 Mathematics question
Let a circle C of radius 5 lie below the x-axis. The line : 4x + 3y + 2 = 0 passes through the centre P of the circle C and intersects the line : 3x − 4y − 11 = 0 at Q. The line touches C at the point Q. Then the distance of P from the line 5x − 12y + 51 = 0 is .
Answer: 11
Solution
Q is the intersection of and : Q = (1, −2). The centre P lies on , P = (x, −(2 + 4x)/3), at distance 5 from Q: ( + 2)/3 − , i.e. ($x -
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