What is the radius of the circle represented by the equation x^2 + y^2 - 6x + 4y = 12?

General formula of the circle

(x-h)² + (y-k)² =r²

We are going to use formula a² +/-2ab +b² = (a-b)² to complete the squares and to write the equation in the general form.

x² + y² - 6x + 4y = 12

x² - 6x + y² + 4y = 12

x² - 2*3x + 3² - 3² + y² +2*2y + 2² - 2² = 12

(x-3)² - 9 + (y+2)² - 4 =12

(x-3)² + (y+2)² = 12 + 13

(x-3)² + (y+2)² = 25

(x-3)² + (y+2)² = 5²

This circle has center (3,-2) and radius = 5.

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints

just needed some points but try socratic