Question

percises 12.5 eld complete the following: Find the intercepts and domain, and perform the way the (a) 16r2 + 25y? = 400 (c) x² + 4y24 (e) 4x² + y² = 64 (g) 9x' + 4y = 36 b) - (a) 4 (h) 7x112 Graph the vertices, foci, endpoints of the

Answer 1

We will have the following:

e)

`4x^2+y^2=64`

From this we will find the x & y-intercepts as follows:

*x-intercepts: We replace y = 0 to find them, that is:

`4x^2+(0)^2=64\Rightarrow4x^2=64\Rightarrow x^2=16\Rightarrow\begin{cases}x=4 \\ x=-4\end{cases}`

So, the x-intercepts are located at (4, 0) & (-4, 0)

*y-intercepts: We replace x = 0 to find them, that is:

`4(0)^2+y^2=64\Rightarrow\begin{cases}y=8 \\ y=-8\end{cases}`

So, the y-intercepts are located at (0, 8) & (0, -8).

*The domain is [-4, 4] and the range is [-8, 8].

*We graph it as follows: