Find the coordinate of the point on the y axis which at a distance of $10$ units from the point $(- 8, 4)$

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Solution

Let the required point be (0,y)
$10^{2} = (0 + 8)^{2} + (4 - y)^{2}$
$\Rightarrow 100 = 64 + 16 + y^{2} - 8 y$
$\Rightarrow 16 + y^{2} - 8 y = 36$
$\Rightarrow y^{2} - 8 y - 20 = 0$
$\Rightarrow y^{2} - 10 y + 2 y - 20 = 0$
$\Rightarrow y (y - 10) + 2 (y - 10) = 0$
$\Rightarrow y = - 2$ or $y = 10$
$∴$ Coordinate of the required point be
$(0, - 2)$ or $(0, 10)$

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Find the coordinate of the point on the y axis which at a distance of 10 units from the point (−8,4)

Let the required point be (0,y)102=(0+8)2+(4−y)2⇒100=64+16+y2−8y⇒16+y2−8y=36⇒y2−8y−20=0⇒y2−10y+2y−20=0⇒y(y−10)+2(y−10)=0⇒y=−2 or y=10∴ Coordinate of the required point be(0,−2) or (0,10)

Find the coordinate of the point on the y axis which at a distance of $10$ units from the point $(- 8, 4)$