Chapter 10: Q. 3 (page 654)

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

Short Answer

Expert verified

$(2, 0), (- 2, 0), (0, - 4) a n d (0, 4)$ are the intercepts for equation $y^{2} = 16 - 4 x^{2}$ .

Step by step solution

Step 1. Given information

Given Expression:

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

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 $x :$

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

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

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 $y :$

$y^{2} = 16 - 4 x^{2} y^{2} = 16 - 4 {(0)}^{2} y^{2} = 16 y = \pm 4$

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

Step 4. Conclusion:

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

$(2, 0), (- 2, 0), (0, - 4) a n d (0, 4)$

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the x-intercepts

Step 3. Finding the y-intercepts:

Step 4. Conclusion:

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Find the intercepts of the equation y2=16-4x2.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the x-intercepts

Step 3. Finding the y-intercepts:

Step 4. Conclusion:

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

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