Question

Which of the following is the equation for the graph shown?

Answer 1

Answer:

y squared over 5 minus x squared over 4 equals 1

Step-by-step explanation:

hope this helps

Answer 2

The equation for the graph is obtained by making use of the relationship

between the directrix and the eccentricity.

Correct response:

• $The \ equation \ of \ the \ graph \ is ; \ \underline{\dfrac{y^2}{5} - \dfrac{x^2}{4} = 1}$

Method by which the above equation is found

The general form of the equation of a vertical hyperbola is given as follows;

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

From the given options, the center of the hyperbola, (h, k) = (0, 0)

The points on the hyperbola are;

$\left(2\frac{1}{4} , \ 0 \right)$, $\left(-2\frac{1}{4} , \, 0 \right )$

(-3, 0) and (3, 0)

The given directrices are;

$y = \frac{5}{3}$ and $y = -\frac{5}{3}$

• $Directrix, \ y = \mathbf{\pm \dfrac{a}{e}}$

• $Eccentricity, \ e = \mathbf{ \dfrac{\sqrt{a^2 + b^2} }{a}}$

Therefore;

• $Directrix, \, y = \mathbf{\dfrac{a^2}{\sqrt{a^2 + b^2} }}$

We have;

a² = 5

√(a² + b²) = 3

Therefore;

5 + b² = 9

b² = 4

• Which gives the equation of the parabola as $\underline{\dfrac{y^2}{5} - \dfrac{x^2}{4} = 1}$, which is the option;

• y squared over 5 minus x squared over 4 equals 1

Learn more about a hyperbola here:

brainly.com/question/2364331