Answered

From beginner to expert, IDNLearn.com has answers for everyone. Discover in-depth and trustworthy answers from our extensive network of knowledgeable professionals.

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.

Match the hyperbolas represented by the equations to their foci.

[tex]\[
\begin{array}{l}
\frac{(x+2)^2}{3^2}-\frac{(y-5)^2}{4^2}=1 \\
\frac{(x-4)^2}{8^2}-\frac{(y+2)^2}{15^2}=1 \\
\frac{(y+5)^2}{15^2}-\frac{(x-1)^2}{8^2}=1 \\
\frac{(x-4)^2}{8^2}-\frac{(y+2)^2}{6^2}=1 \\
\frac{(y-3)^2}{5^2}-\frac{(x-7)^2}{12^2}=1 \\
\frac{(y-3)^2}{5^2}-\frac{(x+7)^2}{12^2}=1 \\
\frac{(y+5)^2}{6^2}-\frac{(x-1)^2}{8^2}=1 \\
\end{array}
\][/tex]

Foci:
[tex]\[
\begin{array}{l}
(1,-22) \text{ and } (1,12) \\
(-7,5) \text{ and } (3,5) \\
(-6,-2) \text{ and } (14,-2) \\
(-7,-10) \text{ and } (-7,16) \\
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Sure, let's pair the equations of the hyperbolas to their corresponding foci:

1. For the equation [tex]\(\frac{(x+2)^2}{3^2}-\frac{(y-5)^2}{4^2}=1\)[/tex]:
- The foci are [tex]\((-7, -10)\)[/tex] and [tex]\((-7, 16)\)[/tex].

2. For the equation [tex]\(\frac{(x-4)^2}{8^2}-\frac{(y+2)^2}{15^2}=1\)[/tex]:
- The foci are [tex]\((-6, -2)\)[/tex] and [tex]\((14, -2)\)[/tex].

3. For the equation [tex]\(\frac{(y+5)^2}{15^2}-\frac{(x-1)^2}{8^2}=1\)[/tex]:
- The foci are [tex]\((1, -22)\)[/tex] and [tex]\((1, 12)\)[/tex].

4. For the equation [tex]\(\frac{(x-4)^2}{8^2}-\frac{(y+2)^2}{6^2}=1\)[/tex]:
- The foci are [tex]\((-7, 5)\)[/tex] and [tex]\((3, 5)\)[/tex].

Let's form the correct pairs:

- [tex]\(\frac{(x+2)^2}{3^2}-\frac{(y-5)^2}{4^2}=1\)[/tex]
- Corresponds to foci: [tex]\((-7, -10)\)[/tex] and [tex]\((-7, 16)\)[/tex]

- [tex]\(\frac{(x-4)^2}{8^2}-\frac{(y+2)^2}{15^2}=1\)[/tex]
- Corresponds to foci: [tex]\((-6, -2)\)[/tex] and [tex]\((14, -2)\)[/tex]

- [tex]\(\frac{(y+5)^2}{15^2}-\frac{(x-1)^2}{8^2}=1\)[/tex]
- Corresponds to foci: [tex]\((1, -22)\)[/tex] and [tex]\((1, 12)\)[/tex]

- [tex]\(\frac{(x-4)^2}{8^2}-\frac{(y+2)^2}{6^2}=1\)[/tex]
- Corresponds to foci: [tex]\((-7, 5)\)[/tex] and [tex]\((3, 5)\)[/tex]

Therefore, the correct matches are:

1. [tex]\(\frac{(x+2)^2}{3^2}-\frac{(y-5)^2}{4^2}=1\)[/tex] with foci [tex]\((-7, -10)\)[/tex] and [tex]\((-7, 16)\)[/tex]
2. [tex]\(\frac{(x-4)^2}{8^2}-\frac{(y+2)^2}{15^2}=1\)[/tex] with foci [tex]\((-6, -2)\)[/tex] and [tex]\((14, -2)\)[/tex]
3. [tex]\(\frac{(y+5)^2}{15^2}-\frac{(x-1)^2}{8^2}=1\)[/tex] with foci [tex]\((1, -22)\)[/tex] and [tex]\((1, 12)\)[/tex]
4. [tex]\(\frac{(x-4)^2}{8^2}-\frac{(y+2)^2}{6^2}=1\)[/tex] with foci [tex]\((-7, 5)\)[/tex] and [tex]\((3, 5)\)[/tex]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Your questions deserve reliable answers. Thanks for visiting IDNLearn.com, and see you again soon for more helpful information.