Chapter 10, Problem 1RE

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

$4x^2+y^2=4$

To determine

If the equation matches with its graph.

Answer to Problem 1RE

Solution: The equation $4x^2+y^2=4$ matches with graph (e).

Explanation of Solution

Given: $4x^2+y^2=4$

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

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

The given equation is:

$4x^2+y^2=4$

Divide throughout by $4$:

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

Rewrite in standard form as:

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

This is of the form:

$\frac{{\left(x-h\right)}^2}{b^2}+\frac{{\left(y-k\right)}^2}{a^2}=1$

Which is the standard equation for an ellipse, whose major axis is vertical.

Thus, the given equation matches with the graph (e).