Equation of an ellipse?

Question

A commercial artist plans to include an ellipse in a design and wants the length of the horizontal axis to equal 10 and the length of the vertical axis to equal 6. Which equation could represent this ellipse?
Choices:
(1) 9x^2+25y^2=225
(2) 9x^2-25y^2=225
(3) x^2+y^2=100
(4) 3y=20x^2

What is the general formula for the equation of an ellipse? Please explain this because I can't find it anywhere.

Thank you for your help!

Answer 1

general form of ellipse:



(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1, where the center is (h , k) , a is the semi-major axis (half of the "long diameter", and b is the semi-minor axis (half of the "short diameter").



Since the long axis is 10, then 2a = 10, a = 5, and a^2 = 25

the short axis is 6, then 2b = 6, b = 3, and b^2 = 9



placing the center at the origin makes this:

x^2 / 25 + y^2 / 9 = 1



doesn't look like any of your choices yet, but try multiplying by 25 * 9 = 225



this gives: 9x^2 + 25y^2 = 225 (yes, choice 1)

Answer 2

general eqn of an ellipse is : x^2/a^2 + y^2/b^2=1, where a is the length of major axis, b is the length of minor axis, and a is not equal to b. only ur first equation is an ellipse (divide both sides by 225), second is a hyperbola, 3d a cirlce, 4th a parabola

Answer 3

(x^2)/5^2 + (y^2)/3^2 = 1



(x^2)/25 + (y^2)/9 = 1



Multiplying through by 225 gives:



9x^2 + 25y^2 = 225



Answer is (1)

Answer 4

1 is an ellipse

2 is a hyperbola

3 is a circle

4 is a parabola

Answer 5

ax²+by²=c is a circle if a=b, and an ellipse otherwise.