The-line-2y-x-3-meets-the-circle-x-2-y-2-2x-6y-15-at-point-M-and-N-where-N-is-in-the-second-quadrant-find-the-coordinate-of-M-and-N-Mastermind-

Question Number 170378 by Mastermind last updated on 22/May/22

T h e l i n e 2 y = x + 3 m e e t s t h e c i r c l e

x^{2} + y^{2} - 2 x - 6 y - 15 a t p o i n t M a n d N

w h e r e N i s i n t h e s e c o n d q u a d r a n t .

f i n d t h e c o o r d i n a t e o f M a n d N .

M a s t e r m i n d

Answered by daus last updated on 22/May/22

x^{2} + y^{2} - 2 x - 6 y = 15

2 y - 3 = x

{(2 y - 3)}^{2} + y^{2} - 2 (2 y - 3) - 6 y = 15

4 y^{2} - 12 y + 9 + y^{2} - 4 y + 6 - 6 y = 15

5 y^{2} - 22 y = 0

y (5 y - 22) = 0

y = 0, 5 y - 22 = 0

y = \frac{22}{5} o r 4.4

x = - 3, x = 5.8

N (- 3, 0) M (5.8, 4.4)

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