$\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\text{ \lparen parallel to the x-axis\rparen} \\ \frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1\text{ \lparen parallel to the y-axis\rparen} \end{gathered}$

Given that the hyperbola has its foci at (0,-15) and (0, 15), this implies that the hyperbola is parallel to the y-axis.

Thus, the equation will be expressed in the form:

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

The asymptote of n hyperbola is expressed as

$y=\pm\frac{a}{b}(x-h)+k$

Given that the asymptotes are

$y=\frac{3}{4}x\text{ and y=-}\frac{3}{4}x$

This implies that

$a=3,\text{ and b=4}$

To evaluate the value of h and k,

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3 0

1 year ago

Which statement is true?

valkas [14]

The answer is J because each one can be proven as false except answer J

4 0

2 years ago

Find the surface area of the figure.<br> PLEASE HELP!

olya-2409 [2.1K]

Answer:

The total surface area is: 468 in^2 which agrees with answer a)

Step-by-step explanation:

The three lateral faces of the prism are rectangles, and the sums of their areas give:

12 * 10 + 9 * 10 + 15 * 10 = 360 in^2

The area of each triangular base (notice it is a right triangle) is given by:

9 * 12 / 2 = 54 in^2, so we add TWO of these to the three rectangular faces:

Total surface = 360 in^2 + 2 * 54 in^2 = 468 in^2

6 0

2 years ago