Question

Find the following compla tvortices for conjugate axis en dansesympates

Answer 1

Hyperbola general formula:

`((x-h)^2)/(a^2)-((y-k)^2)/(b^2)=1`

In this case, the equation is

`(\mleft(x-1\mright)^2)/(4)-((y-2)^2)/(9)=1`

then,

h = 1

k = 2

a = 2

b = 3

Vertices

`\begin{gathered} (h\pm a,k) \\ \text{substituting} \\ (1\pm2,2) \\ (3,2)\text{ and (-1,2)} \end{gathered}`

Foci

`\begin{gathered} (h\pm c,k) \\ c^2=a^2+b^2 \\ c^2=4+9 \\ c=\sqrt[]{13} \\ \text{substituting} \\ (1\pm\sqrt[]{13},2) \\ (1+\sqrt[]{13},2)\text{ and }(1-\sqrt[]{13},2) \end{gathered}`

Conjugate axis endpoints

`\begin{gathered} (h,k\pm b) \\ \text{substituting} \\ (1,2\pm3) \\ (1,5)\text{ and }(1,-1) \end{gathered}`

Asymptotes

`\begin{gathered} y=k\pm(b)/(a)(x-h) \\ \text{substituting} \\ y=2\pm(3)/(2)(x-1) \\ y=2+(3)/(2)(x-1) \\ \text{and} \\ y=2-(3)/(2)(x-1) \end{gathered}`