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Question
Find the equation of tangent to the circle x2 + y2 − 4x + 3y + 2 = 0 at the point (4, −2)
Solution
The equation of tangent to the circle
x2 + y2 + 2gx + 2fy + c = 0, at P(x1, y1) is
xx1 + yy1 + g(x + x1) + f(y + y1) + c = 0 ...(1)
Comparing the equation x2 + y2 – 4x + 3y + 2 = 0 with
x2 + y2 + 2gx + 2fy + c = 0, we get,
2g = – 4, 2f = 3 and c = 2
∴ g = `– 2, "f" = 3/2 and "c" = 2`
∴ from (1), the equation of tangent to the given circle at (4, –2) is
`x(4) + y(-2) -2(x + 4) + 3/2(y - 2) + 2` = 0
∴ `4x - 2y - 2x - 8 + 3/2y - 3 + 2` = 0
∴ `2x - 1/2y - 9` = 0
∴ 4x – y – 18 = 0.
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