Question

Find the intercepts of the equation $y^2=16-4x^2$.

Short answer

$(2,0),(-2,0),(0,-4)and(0,4)$are the intercepts for equation $y^2=16-4x^2$.

Step-by-step solution

Step 1. Given information

Given Expression:

$y^2=16-4x^2$

We want to find the intercepts of the given expression.

Step 2. Finding the x-intercepts

The x-intercept is the point where the graph described with the given equation crosses the x-axis At the point $y=0$

Therefore, set $y=0$and solve the quation for $x:$

$$\begin{gathered} y^2=16-4x^2 \\ 0=16-4x^2 \\ 4x^2=16 \\ {x}^2=4 \\ x=\pm 2 \end{gathered}$$

Therefore, there are two intercepts and they are$(2,0)and(-2,0)$

Step 3. Finding the y-intercepts:

The y-intercept is the point where the graph described with the given equation crosses the y-axis At this point $x=0$.

Therefore, set $x=0$and solve the equation for $y:$

$$\begin{gathered} y^2=16-4x^2 \\ {y}^2=16-4{\left(0\right)}^2{y}^2=16 \\ y=\pm 4 \end{gathered}$$

Therefore there are two y-intercepts and they are$(0,-4)and(0,4).$

Step 4. Conclusion:

To conclude, there are a total of four intercepts for the given equation:

$(2,0),(-2,0),(0,-4)and(0,4)$