Question

Please help me with this problem Please

Answer 1

It may be convenient to get the constant "out of the way" by adding its opposite. Then the square can be completed for both x- and y-terms. The square is completed by adding the squares of half the coefficients of the linear terms.

`x^(2)+y^(2)-10x-14y=26\\\\(x^(2)-10x+5^(2))+(y^(2)-14y+7^(2))=26+5^(2)+7^(2)\\\\(x-5)^(2)+(y-7)^(2)=100\\\\(x-5)^(2)+(y-7)^(2)=10^(2)`

We know the circle with center (h, k) and radius r will have the equation

`(x-h)^(2)+(y-k)^(2)=r^(2)`

By comparing the equation we have with the standard form equation for a circle, the center of the circle and its radius can now be read from the equation.
Center: (5, 7)
Radius: 10