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# Circle

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

Nov 7, 2018

### 1+0 Answers

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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)   Nov 7, 2018