Convert the following standard form to general form of an ellipse.(y-3)²/9+(x-4)²/4=1

Answer 1

(y-3)²/9+(x-4)²/4=1 => general form

Begin by multiplying all terms by both of the denominators to eliminate the fractions. Phew!

4(y-3)^2 + 9(x-4)^2 = 36

Multiply out both of the squared terms.

4(y^2-6y+9) + 9(x^2-8x+16) = 36

Distribute the 4 to the y trinomial and the 9 to the x trinomial.

4y^2-24y+36 + 9x^2-72x+144 = 36

Combine like terms (the constants) and set equal to zero.

4y^2-24y+ 9x^2-72x+144 = 0

Re-order the terms to show an ellipse in general form.

9x^2 + 4y^2 - 72x - 24y + 144 = 0