### Math Notes

Subjects

#### Analytic Geometry Solutions

##### Topics || Problems

Write the equation of the ellipse having an eccentricity equal to 1/3, a distance between foci equal to 2, center at origin and major axis parallel to the x-axis.

$$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$, center at origin and major axis parallel to the x-axis.

$$e = \frac{c}{a}$$

Distance between foci is $$2c$$ thus $$c = 1$$.

$$a = 3$$

$$a^2 = b^2 +c^2$$

$$3^2 = b^2 +1^2$$

$$b = \sqrt{8}$$

Thus the equation of the ellipse is, $$\frac{x^2}{9} + \frac{y^2}{8} = 1$$

$$8x^2 + 9y^2 = 72$$