Find the foci of the ellipse with equation [(x^2)/400]+[(y^2)/625]=1

Question

Find the foci of the ellipse with equation  [(x^2)/400]+[(y^2)/625]=1

imstuck · Answer

First thing, the denominators are squared numbers.  They are known as a and b.  The a is ALWAYS greater than the b, and the a will go under either the x term or they term, and whichever one the a is under is the major axis.  So here, the square root of 400 is 20, and the square root of 625 is 25.  So the a is 25 (a^2 is 625) and it is under the y term, so the major axis is the y axis.  The b is 20 (b^2 is 400) and it is under the x term, so the minor axis is the x axis.  The foci uses the formula a^2 - b^2 = c^2.  So 625 - 400 = c^2-->c^2 = 225-->square root of 225 is 15.  Since this is a y-axis ellipse, the foci points lie on the y axis, at (0, 15) and (0, -15).  I hope this helps!

anonymous · Answer

Oh my gosh that was so clear! Better than my teacher at least...

anonymous · Answer

So following the last bit of your equation the foci of 3x2 + 7y2 = 21 is (0, -2), (0, 2)? or do I have them backwords...