this ellipse is centered at the point (-3, 2). The length of its horizontal axis is 7. What is the ellipse's equation?
here's a photo to help
possible answers either a,b, or c
A. (x+3)^2 (y-2)^2
-------- + -------
7^2 14^2= 1
--------- + ------- = 1
C. (x-6)^2 (y-8)^2
------- + ------ = 1
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A little bit of logic can be used to eliminate some answer possibilities. Recall that a circle is a special case of an ellipse, much like a square is a special case of a rectangle. The formula for a circle with radius \(r\) centered on \((h,k)\) is \[(x-h)^2+(y-k)^2=r^2\]
That immediately rules out C as an answer choice, because the center isn't in the right place.
length of horizontal = 2a
denominator is a^2
To figure out which equation might be correct of the other two, why not set \(y=0\) and see what you get for \(x\)? Experimental learning, it's a good thing...
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B is the correct answer
so the answer would be b ,correct?
You need (x+3)^2 because of the X displacement of 3 so that rules out one of the answers, and you need 3.5^2 as that's the radius of one of the axes so that rules out the other possible choice. Test taking 101!