Find the equation of a circle of radius `5` which lies within the circle `x^2+y^2+14 x+10 y-26=0` and which touches the given circle at the point `(-1,3)dot`

Explanation

To find the equation of a circle of radius 5 that lies within the circle given by the equation \(x^2 + y^2 + 14x + 10y - 26 = 0\) and touches this circle at the point \((-1, 3)\), we will follow these steps:

### Step 1: Rewrite the given circle equation in standard form
The given equation is:
\[ x^2 + y^2 + 14x + 10y - 26 = 0 \]
We will complete the square for both \(x\) and \(y\).
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