A certain circle can be represented by the following equation x^2+y^2+

14x-10y+65=0

What is the center of this circle?

Radius?

for this circle (-7, 5) is the center and 3 is the radius.

Step-by-step explanation:

This is the general equation for the circle, in order to find the center and radius of the circle we need to convert it to the simple form. To do that we must follow a few steps, First we isolate the constant:

x² + y² + 14x - 10y = - 65

We should now group the terms with the same letters:

x² + 14x + y² - 10y = - 65

Now we must factor the number that multiplies the letter that is not squared by two:

(x² + 2*7x) + (y² - 2*5y) = - 65

We now add the factored part powered by two in each parenthesis and do the same on the other side of the equation:

(x²+2*7x + 7²) + (y² - 2*5y + 5²) = - 65 + 7² + 5²

We can see that each parenthesis is in the form of (ax² + 2*a*b*x + b²) or (ax² - 2*a*b*x + b²). Therefore we can factorate them into (ax + b) ² and (ax - b) ²:

(x + 7) ² + (y - 5) ² = - 65 + 49 + 25

(x + 7) ² + (y - 5) ² = 9

Which is in the simple form of the circle equation given by:

(x - x_c) ² + (y - y_c) ² = R²

Where x_c and y_c are the center of the circle and R is the radius. Thefore for this circle (-7, 5) is the center and 3 is the radius.