Find the Eccentricity 25x^2-36y^2=900

$25 x^{2} - 36 y^{2} = 900$

Step 1

Divide each term by $900$ to make the right side equal to one.

$\frac{25 x^{2}}{900} - \frac{36 y^{2}}{900} = \frac{900}{900}$

Step 2

Simplify each term in the equation in order to set the right side equal to $1$ . The standard form of an ellipse or hyperbola requires the right side of the equation be $1$ .

$\frac{x^{2}}{36} - \frac{y^{2}}{25} = 1$

Step 3

This is the standard form of a hyperbola. Use this form to determine the eccentricity.

$\frac{{(x - h)}^{2}}{a^{2}} - \frac{{(y - k)}^{2}}{b^{2}} = 1$

Step 4

Match the values in this hyperbola to those of the standard form. The variable $h$ represents the x-offset from the origin, $k$ represents the y-offset from origin, $a$ .

$a = 6$

$b = 5$

$k = 0$

$h = 0$

Step 5

Find the eccentricity by using the following formula.

$\frac{\sqrt{a^{2} + b^{2}}}{a}$

Step 6

Substitute the values of $a$ and $b$ into the formula.

$\frac{\sqrt{{(6)}^{2} + {(5)}^{2}}}{6}$

Step 7

Simplify the numerator.

Raise $6$ to the power of $2$ .

$\frac{\sqrt{36 + 5^{2}}}{6}$

Raise $5$ to the power of $2$ .

$\frac{\sqrt{36 + 25}}{6}$

Add $36$ and $25$ .

$\frac{\sqrt{61}}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{61}}{6}$

Decimal Form:

$1.30170827 \dots$

Step 9

Find the Eccentricity 25x^2-36y^2=900

Related Questions

Support LCMGCF.com by disabling your adblocker.