Question

1. what are the coordinates of the center of a circle whose equation is ((x + 1)^2 + y^2 = 100)?

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2 = r^2\), where \((h,k)\) is the center of the circle and \(r\) is the radius.

Step2: Compare the given equation with the standard form

The given equation is \((x + 1)^2+y^2=100\). We can rewrite \((x + 1)^2\) as \((x-(- 1))^2\) and \(y^2\) as \((y - 0)^2\). So comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h=- 1\) and \(k = 0\).

Answer:

The coordinates of the center of the circle are \((-1,0)\)