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Find all points where the circle x^2 + y^2 = 25 intersects the line x + 2 = 2y.

 May 4, 2020
 #1
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x^2  + y^2  = 25             x + 2  = 2y  ⇒  x  = 2y - 2

 

Sub the second equation into the first  and we have that

 

(2y - 2)^2  + y^2  =  25       expand

 

4y^2 - 8y + 4  + y^2  = 25  

 

5y^2 - 8y - 21  =  0      factor as

 

(5y + 7) (y - 3)  =  0

 

Setting both factors to 0  and solving for y  produces   y  = -7/5   and y  = 3

 

And when y = -7/5, x  = 2(-7/5) - 2  = -14/5 - 10/5  = -24/5

 

And when y  =  3  ,   x  =2(3) - 2  =  4

 

So....the intersecton points are ( -24/5, -7/5)  and (4, 3)

 

 

cool cool cool

 May 4, 2020

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