Q56 / 90 · JEE Main 2022 (27 Jun Shift 2) · Mathematics

Let a circle C of radius 5 lie below the x-axis. The line L1=4x+3y+2 passes through the centre P of the circle C and intersects the line L2:3x-4y-11=0 at Q. The line L2 touches C at the point Q. Then the distance of P from the line 5x-12y+51=0 is

Correct answer: 11

Solution

Plotting the diagram of given data, we get

Figure

Finding intersection point of 4x+3y+2=0 and 3x-4y-11=0 we get 1,-2

Now finding the point P by parametric we get,Figure

x-1cosθ=y+2sinθ=±5

y=-2+5-45=-6

x=1+535=4

Now finding distance of point P from line 5x-12y+51=0=54-12-6+5113

=20+72+5113

=14313=11

Hence, the correct answer is 11.

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