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| Locus and its equation |
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| There are different ways of defining locus. |
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| i) When a point moves so as to always satisfy a given condition, or conditions, the path it traces out is called its locus under these conditions. |
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| ii) If a point moves according to some given geometrical conditions, then the path traced out by the moving point is called its locus. |
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| iii) The locus of a point is the path traced by it, when it moves under a given condition or conditions. |
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| The locus or graph of a equation in two variables is the curve or straight line containing all the points, and only the points whose coordinates satisfy the equation. |
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| a) Given an equation, to find the corresponding locus. |
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| b) Given a locus under some geometrical condition to determine the corresponding equation. |
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| The following properties of the curve will be very helpful in determining the full form of locus equation. |
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| i) Intercept: The intercept of a curve are the directed distances from the origin to the point where the curve cuts coordinates axes. |
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| In the figure, OA and OB are the intercepts. |
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| a = OA = intercept on x-axis, b = OB = intercept on y-axis. |
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| In figure (1), 'a' and 'b' are both positive. |
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| In figure (2), 'a' is negative and 'b' is positive. |
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| In figure (3), 'a' and 'b' are both negative. |
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| In figure (4), 'a' is positive and 'b' is negative. |
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| Example: |
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| A point (x, y) moves in such a way that its distance from A (3, -2) is always 6. Find the locus. |
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| Suggested answer: |
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| (This is a circle with centre (3,-2) and radius 6.) |
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