Change from General Conic Form to Standard Form: 137+64y=-y^2-x^2-24x

(x + 12) ² + (y + 32) ² = 1031

Step-by-step explanation:

137 + 64y = - y² - x² - 24x

Arrange the terms in descending powers of x and y.

x² + 24x + y² + 64y = - 137

Complete the squares for x and y

(x² + 24x + 144) + (y² + 64y + 1024) = - 137 + 144 + 1024

Write the equation as the squares of binomials of x and y

(x + 12) ² + (y + 32) ² = 1031

This is the equation of a circle with centre at (-12, - 32) and radius r = √1031.