Thread: Equation of Ellipse in Standard Form

I have to write the equation in standard form of the ellipse with foci (8,0) and (-8,0) if the minor axis has y-intercepts of 2 and -2.

I know that the standard form of the equation if x^2/a^2 + y^2/b^2 =1.

This is a horizontal elipse with center (0,0). The length of the minor axis is 4 units so I think c = 4 and c^2 = 16. I don't know where to go to find a^2 and b^2.

Can you help? Thanks.

Joanie

Originally Posted by Joanie

I have to write the equation in standard form of the ellipse with foci (8,0) and (-8,0) if the minor axis has y-intercepts of 2 and -2.

I know that the standard form of the equation if x^2/a^2 + y^2/b^2 =1.

In any ellipse, the distance between the center of the ellipse and either focus is You know (it is half the length of the minor axis), and you know the distance between the center and the foci. So you can solve for

Thanks. I will do the problem and have you check my answer.

Joanie

Originally Posted by Joanie

I have to write the equation in standard form of the ellipse with foci (8,0) and (-8,0) if the minor axis has y-intercepts of 2 and -2.

I know that the standard form of the equation if x^2/a^2 + y^2/b^2 =1.

This is a horizontal elipse with center (0,0). The length of the minor axis is 4 units so I think c = 4 and c^2 = 16. I don't know where to go to find a^2 and b^2.

Can you help? Thanks.

Joanie

Hi Joanie,



The two foci are (-c, 0) and (+c, 0).

So c would have to be 8, wouldn't it? Not 4.

The y-intercepts are at (0, b) and (0, -b) so b would have to be 2 and .

Using , you can easily solve for .

Now just plug and chug.