Changing to standard ellipse form

Question

 change the equation below to standard form of an ellipse what conic does this represent? identify all the elements necessary to graph y. 4x^2+9y^2-8x+36y+4=0 and graph it

Answer 1

4x² + 9y² - 8x + 36y + 4 = 0

 

4x² - 8x + 4 + 9y² + 36y + 36 = 36

 

2²(x - 1)² + 3²(y - 2)² = 6²

 

(x - 1)²/3² + (y - 2)²/2² = 1

 

This is an Ellipse.

 

The elements necessary for graphing are

 

Center: (1,2)

 

Semiaxes: a = 3, b = 2.