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Question

The equations of the tangents to the circle x2+y2 - 4x - 6y - 12 = 0 and parallel to 4x - 3y = 1 are

A
4x + 3y + 14 = 0, 4x + 3y + 16 = 0
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B
4x – 3y – 24 = 0, 4x – 3y + 26 = 0
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C
x – y – 14 = 0, x – y + 16 = 0
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D
4x – 3y + 34 = 0, 4x – 3y + 16 = 0
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Solution

The correct option is B 4x – 3y – 24 = 0, 4x – 3y + 26 = 0
For the circle x2+y2 - 4x - 6y - 12 = 0, centre is (2, 3), radius = 5
Equation of a line parallel to 4x - 3y = 1 is 4x - 3y + k = 0
4x - 3y + k = 0 is a tangent to the circle |4(2)3(3)+k|5 = 5 |k1| = 25 k = 1 ± 25
k = 26 or - 24.
Required tangents are 4x - 3y + 26 = 0, 4x - 3y - 24 = 0

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