List the intercept(s) of the following equation.

Select the correct choice below and, if necessary, fill in the answer box to complete your ch
A. The intercept(s) is/are
(Type an ordered pair. Use a comma to separate answers as needed.)
B. There are no intercepts.

Question

List the intercept(s) of the following equation.

Select the correct choice below and, if necessary, fill in the answer box to complete your ch
A. The intercept(s) is/are
(Type an ordered pair. Use a comma to separate answers as needed.)
B. There are no intercepts.

UpStudy AI · Accepted Answer

To find the intercepts of the equation $$ 4x^2 + 16y^2 = 64 $$, we can first rewrite it in a more standard form by dividing the entire equation by 64:

$$
\frac{4x^2}{64} + \frac{16y^2}{64} = 1
$$

This simplifies to:

$$
\frac{x^2}{16} + \frac{y^2}{4} = 1
$$

This is the equation of an ellipse centered at the origin.

### Finding the x-intercepts:
To find the x-intercepts, we set $$ y = 0 $$:

$$
\frac{x^2}{16} + \frac{0^2}{4} = 1 \implies \frac{x^2}{16} = 1 \implies x^2 = 16 \implies x = \pm 4
$$

Thus, the x-intercepts are $$ (4, 0) $$ and $$ (-4, 0) $$.

### Finding the y-intercepts:
To find the y-intercepts, we set $$ x = 0 $$:

$$
\frac{0^2}{16} + \frac{y^2}{4} = 1 \implies \frac{y^2}{4} = 1 \implies y^2 = 4 \implies y = \pm 2
$$

Thus, the y-intercepts are $$ (0, 2) $$ and $$ (0, -2) $$.

### Summary of intercepts:
The intercepts of the equation are:
- x-intercepts: $$ (4, 0) $$ and $$ (-4, 0) $$
- y-intercepts: $$ (0, 2) $$ and $$ (0, -2) $$

### Final Answer:
A. The intercept(s) is/are $$ (4, 0), (-4, 0), (0, 2), (0, -2) $$
A. The intercepts are $$ (4, 0), (-4, 0), (0, 2), (0, -2) $$

List the intercept(s) of the following equation.

Select the correct choice below and, if necessary, fill in the answer box to complete your ch
A. The intercept(s) is/are
(Type an ordered pair. Use a comma to separate answers as needed.)
B. There are no intercepts.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Finding the x-intercepts:

Finding the y-intercepts:

Summary of intercepts:

Final Answer:

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions

List the intercept(s) of the following equation. Select the correct choice below and, if necessary, fill in the answer box to complete your ch A. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no intercepts.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Finding the x-intercepts:

Finding the y-intercepts:

Summary of intercepts:

Final Answer:

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions

List the intercept(s) of the following equation.

Select the correct choice below and, if necessary, fill in the answer box to complete your ch
A. The intercept(s) is/are
(Type an ordered pair. Use a comma to separate answers as needed.)
B. There are no intercepts.