The equation of a circle is 4x2 + 4y 2− 24x − 32y - 96 = 0. Write the equation in standard form.Question 7Select one:a.(x - 3)2 + (y - 4)2 = 49b.(x - 3)2 + (y + 4)2 = 49c.(x + 3)2 + (y - 4)2 = 49d.(x - 3)2 + (y - 4)2 = -49
Question
The equation of a circle is 4x2 + 4y 2− 24x − 32y - 96 = 0. Write the equation in standard form.Question 7Select one:a.(x - 3)2 + (y - 4)2 = 49b.(x - 3)2 + (y + 4)2 = 49c.(x + 3)2 + (y - 4)2 = 49d.(x - 3)2 + (y - 4)2 = -49
Solution
The standard form of a circle's equation is (x-h)² + (y-k)² = r², where (h,k) is the center of the circle and r is the radius.
Given the equation 4x² + 4y² - 24x - 32y - 96 = 0, we can rewrite it as:
4(x² - 6x) + 4(y² - 8y) = 96
Divide the entire equation by 4 to simplify:
x² - 6x + y² - 8y = 24
To complete the square, we take half of the coefficient of x, square it and add it to both sides. We do the same for y:
x² - 6x + 9 + y² - 8y + 16 = 24 + 9 + 16
This simplifies to:
(x - 3)² + (y - 4)² = 49
So, the answer is (a) (x - 3)² + (y - 4)² = 49.
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