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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Matching In Exercises 1-6, match the equation with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).]

Chapter 10, Problem 1RE, Matching In Exercises 1-6, match the equation with its graph. [The graphs are labeled (a), (b), (c), , example  1

Chapter 10, Problem 1RE, Matching In Exercises 1-6, match the equation with its graph. [The graphs are labeled (a), (b), (c), , example  2

To determine

If the equation 4x2+y2=4 matches with its graph:

Calculus, Chapter 10, Problem 1RE , additional homework tip  1

Answer

Solution:

The equation 4x2+y2=4 matches with graph (e) and the graph is

Calculus, Chapter 10, Problem 1RE , additional homework tip  2

Explanation

Given:

The options are:

Calculus, Chapter 10, Problem 1RE , additional homework tip  3

Explanation:

Here, x and y both are squared terms and both of their coefficients are positive. Thus, this equation represents an ellipse.

Now, in order to find whether the ellipse is horizontal or vertical, represent the equation in the standard form of an ellipse.

The given equation is:

4x2+y2=4

Divide the equation by 4:

x2+14y2=1

Rearrange it in standard form as:

x212+y222=1

So,

(xh)2b2+(yk)2a2=1

Which is the standard equation for an ellipse, whose major axis is vertical. That is the center of ellipse is (h,k)=(0,0) with semi axis a=1,b=2, focus is (0,3) and vertex be (0,2)

Thus, the correct graph matches for the equation that holds the above properties is option (e).

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