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Question
Determine whether the points P(1, 0), Q(2, 1) and R(2, 3) lie outside the circle, on the circle or inside the circle x2 + y2 – 4x – 6y + 9 = 0.
Solution
The equation of the circle is x2 + y2 – 4x – 6y + 9 = 0
`"PT"^2 = x_1^2 + y_1^2 - 4x_1 - 6y_1 + 9`
At P(1, 0), PT2 = 1 + 0 – 4 – 0 + 9 = 6 > 0
At Q(2, 1), PT2 = 4 + 1 – 8 – 6 + 9 = 0
At R(2, 3), PT2 = 4 + 9 – 8 – 18 + 9 = -4 < 0
The point P lies outside the circle.
The point Q lies on the circle.
The point R lies inside the circle.
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