Question

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Find a relation between x and y such that the point P(x, y) is equidistant from the points A (2, 5) and B (-3, 7). ​

Answer 1

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Find a relation between x and y such that the point P(x, y) is equidistant from the points A (2, 5) and B (-3, 7).

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Let P (x, y) be equidistant from the points A (2, 5) and B (-3, 7).

∴ AP = BP …[Given

AP2 = BP2 …[Squaring both sides

(x – 2)2 + (y – 5)2 = (x + 3)2 + (y – 7)2

⇒ x2 – 4x + 4 + y2 – 10y + 25

⇒ x2 + 6x + 9 + y2 – 14y + 49

⇒ -4x – 10y – 6x + 14y = 9 +49 – 4 – 25

⇒ -10x + 4y = 29

∴ 10x + 29 = 4y is the required relation.

Answer 2

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Let P (x, y) be equidistant from the points A (2, 5) and B (-3, 7).

∴ AP = BP …[Given

AP2 = BP2 …[Squaring both sides

(x – 2)2 + (y – 5)2 = (x + 3)2 + (y – 7)2

⇒ x2 – 4x + 4 + y2 – 10y + 25

⇒ x2 + 6x + 9 + y2 – 14y + 49

⇒ -4x – 10y – 6x + 14y = 9 +49 – 4 – 25

⇒ -10x + 4y = 29

∴ 10x + 29 = 4y is the required relation.