Question

find a point on the y axis egudistant from (-5,2)and (9,-2)

Answer 1

$\text{Answer : } \\ \\ \text{Let, the point on y - axis be (0, y)}\\ \\ \text {Then, the distance between the points } \\ \text{(0, y) and ( - 5, 2) is} \\ = \sqrt{ { \{0 - ( -5 ) \}}^{2} + {( \text{y} - 2)}^{2} } \\ = \sqrt{25 + { \text{y}}^{2} - \text{4y} + 4} \\ = \sqrt{ { \text{y}}^{2} - \text{4y} + 29 } \: \: \text{units}\\ \\ \text{and the distance between the points} \\ \text{(0, y) and (9, - 2) is} \\ = \sqrt{ {(0 - 9)}^{2} + { \{ \text{y} -( - 2) \} }^{2} } \\ = \sqrt{81 + { \text{y}}^{2} + \text{4y} + 4 } \\ = \sqrt{ { \text{y}}^{2} + \text{4y} + 85 } \: \: \text{units} \\ \\ \text{By the given condition,} \\ \sqrt{ { \text{y}}^{2} - \text{4y} + 29 } = \sqrt{ { \text{y}}^{2} + \text{4y} + 85 } \\ \\ \text{Squaring both sides, we get} \\ { \text{y}}^{2} - \text{4y} + 29 = { \text{y}}^{2} + \text{4y} + 85 \\ \to \text{4y + 4y = 29 - 85} \\ \to \text{8y = - 56} \\ \to \text{y} = - \frac{56}{8} \\ \therefore \text{y = - 7 } \\ \\ \therefore \text{The required point on y - axis is (0, - 7).}$