Question

Write the standard form for an ellipse: 9x² + 25y² + 90x + 100y + 100 = 0.

a) ((x-5)²)/25 + ((y+2)²)/9 = 1
b) ((x+5)²)/25 + ((y-2)²)/9 = 1
c) ((x-5)²)/9 + ((y+2)²)/25 = 1
d) ((x+5)²)/9 + ((y-2)²)/25 = 1

Answer 1

The standard form for the given ellipse equation is ((x+5)²)/9 + ((y+2)²)/25 = 1.

so the correct answer is option a).

Step-by-step explanation:

The given equation, 9x² + 25y² + 90x + 100y + 100 = 0, can be rearranged to the standard form of an ellipse.

To do this, we have to complete the square for both the x and y terms. First, we divide the equation by the constant term to make it easier to work with, giving us x²/9 + y²/25 + 10x/9 + 4y/25 + 10/9 = 0.

Next, we group the x and y terms separately and complete the square for each group. For the x terms, we have x²/9 + 10x/9, which can be written as (x+5)²/9. For the y terms, we have y²/25 + 4y/25, which can be written as (y+2)²/25.

Putting it all together, we get the standard form of the ellipse as ((x+5)²)/9 + ((y+2)²)/25 = 1, so the correct answer is option a).