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the equation of the circle is:(x+5)^2+(y-6)^2 = 25

 Nov 7, 2018
 #1
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In the equation of the circle.....sub   2x + 11   for y......and we have

 

( x + 5)^2  +  (  2x + 11 - 6)^2   =  25      simplify

 

x^2 + 10x  +  25   + ( 2x + 5)^2   =  25

 

x^2 + 10x + 25 +  4x^2 + 20x + 25  = 25

 

5x^2 + 30x + 50  = 25        subtract 25 from both sides

 

5x^2 + 30 x + 25   = 0         factor out 5

 

5 ( x^2 + 6x + 5)   =  0       divide both sides by 5

 

x^2 + 6x + 5   = 0

 

 

Factor  x^2 + 6x + 5  =  0     as

 

(x + 5) ( x + 1)  = 0

 

Set each factor to 0  and solve for x and we have

 

x = - 5      and  x  =  - 1

 

These are the x coordinates of the intersections...and the y coordinates are

 

y = 2(-5) + 11  = 1        and    y = 2(-1) + 11  =  9

 

So...the intersection points are

 

(-5, 1)   and ( -1, 9)

 

 

 

cool cool cool

 Nov 7, 2018

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