The general form of a circle's equation is x² + y² + Dx + Ey + F = 0, and the standard form 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 x² + y² + 6x - 10y - 15 = 0, we can rearrange it to group the x terms and y terms together:

(x² + 6x) + (y² - 10y) = 15

To convert this into the standard form, we need to complete the square for both the x terms and the y terms.

For the x terms, the number we add to both sides to complete the square is (6/2)² = 9. For the y terms, the number we add is (-10/2)² = 25.

So, we get:

(x² + 6x + 9) + (y² - 10y + 25) = 15 + 9 + 25

This simplifies to:

(x + 3)² + (y - 5)² = 49

So, the standard form of the given equation is (x + 3)² + (y - 5)² = 49.

Therefore, the correct answer is b. (x + 3)² + (y - 5)² = 49.

Question

The general form of a circle's equation is x² + y² + Dx + Ey + F = 0, and the standard form 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 x² + y² + 6x - 10y - 15 = 0, we can rearrange it to group the x terms and y terms together:

(x² + 6x) + (y² - 10y) = 15

To convert this into the standard form, we need to complete the square for both the x terms and the y terms.

For the x terms, the number we add to both sides to complete the square is (6/2)² = 9. For the y terms, the number we add is (-10/2)² = 25.

So, we get:

(x² + 6x + 9) + (y² - 10y + 25) = 15 + 9 + 25

This simplifies to:

(x + 3)² + (y - 5)² = 49

So, the standard form of the given equation is (x + 3)² + (y - 5)² = 49.

Therefore, the correct answer is b. (x + 3)² + (y - 5)² = 49.

Knowee AI · Accepted Answer

The general form of a circle's equation is x² + y² + Dx + Ey + F = 0, and the standard form 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 x² + y² + 6x - 10y - 15 = 0, we can rearrange it to group the x terms and y terms together:

(x² + 6x) + (y² - 10y) = 15

To convert this into the standard form, we need to complete the square for both the x terms and the y terms.

For the x terms, the number we add to both sides to complete the square is (6/2)² = 9. For the y terms, the number we add is (-10/2)² = 25.

So, we get:

(x² + 6x + 9) + (y² - 10y + 25) = 15 + 9 + 25

This simplifies to:

(x + 3)² + (y - 5)² = 49

So, the standard form of the given equation is (x + 3)² + (y - 5)² = 49.

Therefore, the correct answer is b. (x + 3)² + (y - 5)² = 49.

Convert the general form equation of the circle into the standard form: x2 + y2 + 6x - 10y - 15 = 0Question 8Select one:a.(x + 3)2 + (y - 5)2 = 361b.(x + 3)2 + (y - 5)2 = 49c.(x + 3)2 + (y - 5)2 = 7d.(x + 6)2 + (y - 10)2 = 225

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