Question

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.

Answer 1

Answer:

The equation of the ellipse is $\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1$

Step-by-step explanation:

Let the equation of the ellipse is $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ {As the center of the ellipse is at the origin}

Therefore, the vertices of the ellipse are (± a,0) and foci are (± ae,0)

Now, given that a = 3 and ae = 2

Now, eccentricity of a ellipse is given by b² = a² - a²e² = 3² - 2² = 5

Therefore, the equation of the ellipse is $\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1$ (Answer)