109k views
5 votes
Determine the equation of the ellipse with center (10,-8), a focus at (10, -14),

and a vertex at (10, -18).

Determine the equation of the ellipse with center (10,-8), a focus at (10, -14), and-example-1
User Eralper
by
7.8k points

1 Answer

7 votes

Answer:

(x -10)²/64 +(y +8)²/100 = 1

Explanation:

You want the equation of the ellipse with center (10,-8), a focus at (10, -14), and a vertex at (10, -18).

Axes

The length of the semi-major axis is the distance between the center and the give vertex: a = -8 -(-18) = 10 units.

The distance from the center to the focus is -8 -(-14) = 6.

The distance from the center to the covertex is the other leg of the right triangle with these distances as the hypotenuse and one leg.

b = √(10² -6²) = √64 = 8 . . . . units

Equation

The equation for the ellipse with semi-axes 'a' and 'b' with center (h, k) is ...

(x -h)²/b² +(y -k)²/a² = 1

(x -10)²/64 +(y +8)²/100 = 1

__

Additional comment

The center, focus, and given vertex are all on the vertical line x=10, This means the major axis is in the vertical direction, and the denominator of the y-term will be the larger of the two denominators.

You will notice the center-focus-covertex triangle is a 3-4-5 right triangle with a scale factor of 2.

Determine the equation of the ellipse with center (10,-8), a focus at (10, -14), and-example-1
User Kovy Jacob
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories