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Determine whether the points (-2, 1), (0, 0) and (-4, -3) lie outside, on or inside the circle x2 + y2 – 5x + 2y – 5 = 0. |
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Answer» To find the position of a point with regard to a given circle, substitute the point in the equation of the circle if we get a positive value, the point lies outside the circle. If we get a -ve value the point lies inside the circle and if we get O then the point lies on the circumference of the circle. The given circle is x2 + y2 – 5x + 2y – 5 = 0 ... (1) Substituting the point (-2, 1) in (1) we get 4 + 1 – 5(-2) + 2(1) – 5 = 5 + 10 + 2 – 5 = 12 ⇒ (- 2, 1) lies outside the circle Substituting the point (0, 0) in (1) we get -5 < 0 ⇒ (0, 0) lies inside the circle Substituting the point (-4, -3) in (1) we get 16 + 9 + 20 – 6 – 5 = 34 > 0 ⇒ (- 4, -3) lies outside the circle |
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