the answer i got was x²/25 + y²/16 = 1 ... can anyone confirm for me? please and thanks.
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Note that the ellipse is centered at the origin since the foci have the form (±c, 0). Also, since the foci lie along the x-axis, the major axis will be horizontal.
Since the foci are at (±3, 0), we see that c = 3. Then, the major axis is 10 units long:
2a = 10 ==> a = 5.
Then, since c^2 = a^2 - b^2:
3^2 = 5^2 - b^2 ==> b = 4.
Thus, the equation is:
x^2/5^2 + y^2/4^2 = 1 ==> x^2/25 + y^2/16 = 1.
So, you are correct!
I hope this helps!
Since the foci are at (±3, 0), we see that c = 3. Then, the major axis is 10 units long:
2a = 10 ==> a = 5.
Then, since c^2 = a^2 - b^2:
3^2 = 5^2 - b^2 ==> b = 4.
Thus, the equation is:
x^2/5^2 + y^2/4^2 = 1 ==> x^2/25 + y^2/16 = 1.
So, you are correct!
I hope this helps!