Question
A circular pond is modeled by the equation x^2+y^2= 225. A bridge over the pond is modeled by a segment of the equation x–7y=–75. What are the coordinates of the points where the bridge meets the edge of the pond?
Can you teach me how to do this?
Can you teach me how to do this?
Answers
Reiny
from the linear equation: x = 7y - 75
intersect the two relations,
x^2 + y^2 = 225
(7y-75)^2 + y^2 - 225 = 0
49y^2 - 1050y + 5625 + y^2 - 225 = 0
50y^2 - 1050y + 5400 = 0
divide by 50
y^2 - 21y + 108 = 0
(y - 12)(y - 9) = 0
y = 12 or y = 9
if y = 12, x = 9
if y = 9 , x = -12
the bridge meets the point at (9,12) and (-12,9)
verification by Wolfram:
http://www.wolframalpha.com/input/?i=plot+x%5E2%2By%5E2%3D+225+%2C+x%E2%80%937y%3D%E2%80%9375+from+-15+to+15
intersect the two relations,
x^2 + y^2 = 225
(7y-75)^2 + y^2 - 225 = 0
49y^2 - 1050y + 5625 + y^2 - 225 = 0
50y^2 - 1050y + 5400 = 0
divide by 50
y^2 - 21y + 108 = 0
(y - 12)(y - 9) = 0
y = 12 or y = 9
if y = 12, x = 9
if y = 9 , x = -12
the bridge meets the point at (9,12) and (-12,9)
verification by Wolfram:
http://www.wolframalpha.com/input/?i=plot+x%5E2%2By%5E2%3D+225+%2C+x%E2%80%937y%3D%E2%80%9375+from+-15+to+15