An equation (from the chooses) for an ellipse with center at (1, 1) and major axis parallel to the x-axis.?

Question

equations to choose from....

a. 4x^2 + 9y^2 - 8x + 18y - 23 = 0
b. 9x^2 + 4y^2 - 18x + 8y - 23 = 0
c. 4x^2 + 9y^2 + 8x - 18y - 23 = 0
d. 9x^2 + 4y^2 + 18x - 8y - 23 = 0
e. 4x^2 + 9y^2 - 8x - 18y - 23 = 0
f. 9x^2 + 4y^2 - 18x - 8y - 23 = 0
g. none of these

Answer 1

rather than put all 6 into standard form, let's think about it. it's going to look like (x-1)²/a² + (y-1)²/b² = 1. so first of all the x coefficient will be -2 times the x² coefficient, and same for y's. that rules out a (+18y), b (+8y), c (+8x), and d (+18x).

then to make the major axis parallel to x axis, need the a² > b², which makes, when you multiply by lcd, a² the y² coefficient, so the answer is e.