Find the points on the y-axis, each of which is at a distance of 13 units from the point (-5, 7).

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Solution

Let A (-5, 7) be the given point and let P (0, y) be the required point on the y-axis. Then,

$P A = 13 u n i t s ⟹ P A^{2} = 169 u s i n g t h e d i s t a n c e f o r m u l a w e c a n w r i t e ⟹ (0 + 5)^{2} + (y - 7)^{2} = 169 ⟹ 25 + y^{2} - 14 y + 49 = 169 ⟹ y^{2} - 14 y + 74 = 169 ⟹ y^{2} - 14 y - 95 = 0 ⟹ (y - 19) (y + 5) = 0 ⟹ y - 19 = 0 o r, y + 5 = 0 ⟹ y = 19 o r, y = - 5 H e n c e, t h e r e q u i r e d p o i n t s a r e (0, 19) a n d (0, - 5)$

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