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

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Solution

Let the points be $(0, y)$

Given: Distance is $B$ units

Distance between the points $(- 5, 7)$ and $(0, y) = B$

$\Rightarrow \sqrt{25 + (y - 7)^{2}} = B$

$\Rightarrow 25 + (y - 7)^{2} = B^{2}$

$\Rightarrow y^{2} - 14 y + 49 = B^{2} - 25$

$\Rightarrow y^{2} - 14 y - B^{2} + 74 = 0$

Using the formula for roots $= \frac{- b \pm b^{2} - 4 a c}{2 a}$

$\Rightarrow y = 7 \pm \sqrt{B^{2} - 25}$

Therefore, points are $(0, 7 + \sqrt{B^{2} - 25})$ and $(0, 7 - \sqrt{B^{2} - 25})$

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