Question

 

Write an equation for an ellipse with center (1,-3) vertices (1,2) andd (1,-8) and co-vertices (4,-3) and (-2,-3)?

Answer 1

Standard form of ellipse with horizontal major axis: (x-h)²/a²+(y-k) 2/b²=1, (a>b), with (h, k) being the (x, y) coordinates of the centre.

Standard form of ellipse with vertical major axis: (x-h)²/b²+(y-k)²/a²=1, (a>b), with (h, k) being the (x, y) coordinates of the centre.

The difference between the two forms is the interchange of a² and b².

Given centre at (1, -3)
Since the x-coordinates of the end points of the vertices are the same at 1, given ellipse has a vertical major axis on x=1.

Length of major axis = 10 = 2a
a = 5.

a²=25

co-vertices or minor axis on y = -3
length of minor axis = 6 = 2b
b=3
b²=9

Equation: (x-1)²/9+(y+3)²/25 =1

 

source: http://www.algebra.com