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-

Question Number 127652 by faysal 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}

Facebook Tweet Pin