Sum of axis of ellipse given by equation

Question

9x^2 + 25y^2 - 36x - 50y - 164 = 0 is?  

 

 

Answer 1

The ellipse equation 

To change the expressions (x ²- 4x) and (y ² - 2y) into a perfect square trinomial,

add (half the x coefficient)² and add (half the y coefficient)² to each side of the equation

The standard form for an ellipse is in a form = 1, So divide both sides of equation by 225 to set it equal to 1.

Compare it to standard form of ellipse

a ² > b ²

If the larger denominator is under the "x " term, then the ellipse is horizontal.

center (h, k ) = (2, 1)

a  = length of semi-major axis .

b  = length of semi-minor axis .

a = 5, b = 3

Major  axis 2a = 2* 5 = 10

Minor axis 2b = 2*3 = 6

Sum of axis of ellipse = 10 + 6 =  16.

Sum of axis of ellipse = 16.