How do you find the standard form of the equation of the ellipse given the properties foci #(+-3,0)#, length of the minor axis 10?

1 Answer
May 31, 2017

Answer:

#x^2/109 + y^2/100 = 1#

Explanation:

Let #a = "major axis"#, #b = "minor axis"# and #c = 1/2*"focal length"#

#b = 10# is given.

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Since our foci are both #3# away from the origin and lie on the x-axis, the center of the ellipse will be at the origin. We also know that #c = 3#, then.

Using the property of ellipses that:

#a^2= b^2 + c^2#

We can determine the value of #a#, the major axis.

#a^2 = 10^2+3^2#

#a^2 = 109#

Let's stop there, since our final equation relies on #a^2# rather than #a#.

Now, we have everything we need to make the standard form equation for the given ellipse. Here is what standard form looks like for an ellipse with a horizontal major axis:

#(x-h)^2/a^2 + (y-k)^2/b^2 = 1#

Where #(h,k)# is the center of the ellipse. However, in this case, the center is #(0,0)#, so we don't even need to worry about #h# and #k#.

Therefore, this specific ellipse's equation is:

#x^2/109 + y^2/100 = 1#

Final Answer