+466 x2 + 2y2 - 10x + 8y + 29 = 0 is the general equation of an ellipse. Write the equation of this ellipse in standard form and give the coordinates of the center, the length of the major axis, and the length of the minor axis.
Please help, I need this procedure broken down for me.
+128475 x^2 + 2y^2 - 10x + 8y + 29 = 0
We need to put this in standard form which is :
(x - h)^2 + (y - k)^2 = 1
a^2 b^2
Shades, we need to complete the square on x and y, first......rearranging and factoring out the lead coefficient on y^'2,, we have
x^2 - 10x + 25 + 2(y^2 + 4y + 4 ) = -29 + 25 + 8 factor
(x - 5)^2 + 2(y + 2)^2 = 4 divide through by 4
( x - 5)^2 + (y + 2)^2 = 1
4 2
This is now in standard form
The center is ( 5 , -2)
The major axis lies along x..... and its length is given by 2a = 2(2) = 4
The minor axis lies along y... and its length is given by 2b = 2(sqrt(2) ) = about 2.828
Here's a graph : https://www.desmos.com/calculator/3yrngchn3l
Also...I wasn't able to go into great detail....but....here's something that might help you understand more thoroughlty..... http://www.purplemath.com/modules/ellipse.htm
