Question

Convert the equation from standard form to General form.

(x - 1)2 + (y + 2)2 = 16

Answer 1

x² + y² - 2x + 4y - 11 = 0

Explanation:

Given : (x - 1)² + (y + 2)² = 16

So,

(x - 1)² = (x-1) (x-1) = x(x-1) - 1*(x-1) = x² - x - x + 1 = x² - 2x + 1

(y + 2)² = (y+2) (y+2) = y(y+2) + 2(y+2) = y² + 2y + 2y + 4 = y² + 4y + 4

∴ (x - 1)² + (y + 2)² = 16

x² - 2x + 1 + y² + 4y + 4 = 16

x² + y² - 2x + 4y + 1 + 4 - 16 = 0

x² + y² - 2x + 4y - 11 = 0

So, The General form ⇒ x² + y² - 2x + 4y - 11 = 0