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