Question

What is the equation of the ellipse with foci (7, 0), (-7, 0) and co-vertices (0, 3), (0, -3)?*

a) x²/49 + y²/9= 1
b) x²/9 + y²/49= 1
c) x²/16 + y²/64= 1
d) x²/64 + y²/16= 1

Answer 1

The equation of the given ellipse is x²/49 + y²/9 = 1.

Step-by-step explanation:

To find the equation of the ellipse, we first need to determine the center of the ellipse. The center is the midpoint between the foci, which in this case is (0, 0). Next, we need to find the length of the semi-major axis (a) and the semi-minor axis (b). The semi-major axis is the distance from the center to each vertex, which is 7 units. The semi-minor axis is the distance from the center to each co-vertex, which is 3 units. Now we can write the equation of the ellipse in standard form:

x²/a² + y²/b² = 1

Substituting the values for a and b, we have:

x²/49 + y²/9 = 1

So, the answer is a) x²/49 + y²/9 = 1.