determine the coordinate of a point which is on the 3x−4y+12=0 and the distance of the point from (0,0) is 10 unit


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Question Number 127652 by deleteduser12 last updated on 31/Dec/20

$d e t e r m i n e t h e c o o r d i n a t e o f a p o i n t w h i c h i s o n t h e$ $3 x - 4 y + 12 = 0 a n d t h e d i s t a n c e o f t h e p o i n t f r o m (0, 0)$ $i s 10 u n i t$
	Answered by liberty last updated on 31/Dec/20

	$let the point A (x, y) and distance = \sqrt{x^{2} + y^{2}}$ $x^{2} + y^{2} = 100 \Rightarrow {9 x}^{2} + {9 y}^{2} = 900$ $the line 3 x = 4 y - 12 or {9 x}^{2} = {(4 y - 12)}^{2}$ $we find 900 - {9 y}^{2} = {16 y}^{2} - 96 y + 144$ $\Rightarrow {25 y}^{2} - 96 y - 756 = 0$ $\Rightarrow y = \frac{96 \pm \sqrt{96^{2} + 75600}}{50} = \frac{96 \pm 291.23}{50}$
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