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Find the center and radius of the circle whose equation is x^2+3x+y^2-17 = 0. The center of the circle is ( , ). The radius of the circle is

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Find the center and radius of the circle whose equation is x^2+3x+y^2-17 = 0. The center of the circle is (___ ,___ ). The radius of the circle is_______

Guest Jun 13, 2015

#2
+92159
+10

$$\begin{array}{rll} x^2+3x+y^2-17 &=& 0\\\\ x^2+3x+y^2 &=& 17\\\\ x^2+3x+(\frac{3}{2})^2\;\;+y^2 &=& 17+(\frac{3}{2})^2\\\\ (x+\frac{3}{2})^2\;\;+y^2 &=& 17+\frac{9}{4}\\\\ (x+\frac{3}{2})^2\;\;+y^2 &=& \frac{77}{4}\\\\ (x+\frac{3}{2})^2\;\;+y^2 &=& \left(\frac{\sqrt{77}}{2}\right)^2\\\\ \end{array}\\\\ centre\;\;(\frac{-3}{2},\;0)\qquad radius&=& \frac{\sqrt{77}}{2}$$

Melody  Jun 13, 2015
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#1
+26619
+10

Get this in the form (x - xc)2 + (y - yc)2 = r2

First look at the x-terms

x2 + 3x can be written as (x + 3/2)2 - 9/4  = (x - -3/2)2 - 9/4  giving xc = -3/2

Now look at the y-terms

y2 can be written as (y - 0)2 giving yc = 0

(xc, yc) = (-3/2, 0)

So the original equation can be written as (x + 3/2)2 - 9/4 + (y - 0)2 - 17 = 0

or (x + 3/2)2 + (y - 0)2 = 17 +9/4

or (x + 3/2)2 + (y - 0)2 = 77/4

so r2 = 77/4

r = (√77)/2

.

Alan  Jun 13, 2015
#2
+92159
+10
$$\begin{array}{rll} x^2+3x+y^2-17 &=& 0\\\\ x^2+3x+y^2 &=& 17\\\\ x^2+3x+(\frac{3}{2})^2\;\;+y^2 &=& 17+(\frac{3}{2})^2\\\\ (x+\frac{3}{2})^2\;\;+y^2 &=& 17+\frac{9}{4}\\\\ (x+\frac{3}{2})^2\;\;+y^2 &=& \frac{77}{4}\\\\ (x+\frac{3}{2})^2\;\;+y^2 &=& \left(\frac{\sqrt{77}}{2}\right)^2\\\\ \end{array}\\\\ centre\;\;(\frac{-3}{2},\;0)\qquad radius&=& \frac{\sqrt{77}}{2}$$