anotha killer..........ellipse this time!!?

Question

thanx guys for the circle problem...it was really helpful...
so here it is------ write in both standard and general form the ellipse with a center at (3,2) and a major axis length of 8 units (parallel to x-axis) with a minor axis length of 6 units......

thx guys this is very important........

Answer 1

The standard form of an ellipse is as follows:

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

Where (h,k) is the coordinates of the center, a represents the horizontal diameter and b represents its vertical diameter.

All you have to do is plug in h = 3, k = 2, a = 8, b = 6, to get

[(x - 3)^2]/(8^2) + [(y - 2)^2]/(6^2) = 1

[(x - 3)^2]/64 + [(y - 2)^2]/36 = 1

To solve for the general form, all you have to do is multiply it out and get rid of all fractions.

Answer 2

The equation of an ellipse is in standard form is:

The center of the ellipse is (h,k).
The semi-major axis is a.
The semi-minor axis is b.

Since the major axis is parallel to the x axis, the a and x terms go together. Therefore the y and b terms go together.

(h,k) = (3,2)
a = 8/2 = 4
b = 6/2 = 3

The equation therefore is:

(x - 3)²/4² + (y - 2)²/3² = 1
(x - 3)²/16 + (y - 2)²/9 = 1

Here is the form for the general quadratic equation.

(x - 3)²/16 + (y - 2)²/9 = 1
(x - 3)²/16 + (y - 2)²/9 - 1 = 0
9(x - 3)² + 16(y - 2)² -144 = 0
9(x² - 6x + 9) + 16(y² - 4y + 4) - 144 = 0
9x² - 54x + 81 + 16y² - 64y + 64 - 144 = 0

9x² + 16y² - 54x - 64y + 1 = 0