Question

find the center and the radius of the circle.
$x^{2}+y^{2}+2x - 35 = 0$
center:
radius:
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Explanation:

Step1: Rearrange and complete the square for \(x\) terms

Group \(x\) terms: \((x^{2}+2x)+y^{2}=35\).
Complete the square for \(x\): \(x^{2}+2x=(x + 1)^{2}-1\).
The equation becomes \((x + 1)^{2}-1+y^{2}=35\).

Step2: Write in standard circle form

Simplify to \((x + 1)^{2}+y^{2}=36\).
The standard form of a circle is \((x - h)^{2}+(y - k)^{2}=r^{2}\), where \((h,k)\) is the center and \(r\) is the radius.

Answer:

Center: \((-1,0)\)
Radius: \(6\)