Question

What is the standard form of the ellipse whose equation is 8x^2 +9y^2 – 16x – 9y+2 = 0? Drag an expression into each box to correctly complete the equation. ___ + ___ = 1 32(x-1)^2/33 33 (x-1)^2/32

(x-1)^2/33
12(y-1/2)^2/11
11(y-1/2)^2/12

Answer 1

To get the standard form of the ellipse equation, we complete the square for x and y terms, and the standard form is 33(x-1)^2/32 + 32(y-1/2)^2/33 = 1.

Step-by-step explanation:

To find the standard form of the ellipse equation 8x^2 +9y^2 – 16x – 9y+2 = 0, we first complete the square for the x-terms and y-terms separately. We group the x-terms and y-terms, factor out the coefficients of the squared terms, and then add and subtract the necessary constants to complete the square for each group.

Completing the square for the x-terms, we end up with (x-1)^2, and for the y-terms, we have (y-1/2)^2. We then divide by the coefficients to get the standard form, ensuring that the equation is equal to 1. The result is 33(x-1)^2/32 for the x-part and 32(y-1/2)^2/33 for the y-part.

The standard form of the given ellipse is 33(x-1)^2/32 + 32(y-1/2)^2/33 = 1.