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Chapter 10: Q. 3 (page 654)

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

Short Answer

Expert verified

(2,0),(-2,0),(0,-4)and(0,4)are the intercepts for equation y2=16-4x2.

Step by step solution

01

Step 1. Given information

Given Expression:

y2=16-4x2

We want to find the intercepts of the given expression.

02

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=0and solve the quation for x:

y2=16-4x20=16-4x24x2=16x2=4x=卤2

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

03

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=0and solve the equation for y:

y2=16-4x2y2=16-4(0)2 y2=16y=卤4

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

04

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)

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