Question

Write the equation in standard form. Identity the center and radius.
x² + y2 + 8x-4y-7=0

Answer 1

• See below

Explanation:

Given equation:

• x² + y² + 8x - 4y - 7 = 0

Convert this to standard form by completing the square:

• (x - h)² + (y - k)² = r², where (h, k) - center, r - radius
• x² + 2*4x + 4² + y² - 2*2y + 2² - 16 - 4 - 7 = 0
• (x + 4)² + (y - 2)² - 27 = 0
• (x + 4)² + (y - 2)² = 27
• (x + 4)² + (y - 2)² = (√27)²

The center is (- 4, 2) and the radius is √27