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Question
A point moves so that it is always at a distance of 4 units from the point (3, –2)
Solution
Let P(x1, y1) be any point on the locus.
Let A be the point (3, -2)
Given that PA = 4
PA2 = 16
(x1 - 3)2 + (y1 + 2)2 = 16
`x_1^2 - 6x_1 + 9 + y_1^2 + 4y_1 + 4 = 16`
`x_1^2 + y_1^2 - 6x_1 + 4y_1 - 3 = 0`
∴ The locus of the point (x1, y1) is x2 + y2 – 6x + 4y – 3 = 0
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