Chapter 8, Problem 14RE

Solution

To find:The correct graph for the given equation $\frac{{\left(x-2\right)}^2}{4}+y^2=1$ .

Thereforethe correct graph of the equation is option (g).

Given information:

The equation is $\frac{{\left(x-2\right)}^2}{4}+y^2=1$ .

Calculation:

The given equation is of the form

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

This is the standard equation of ellipse with center $\left(h,k\right)$ .

The given equation can be rewritten as

  $\frac{{\left(x-2\right)}^2}{2^2}+\frac{{\left(y-0\right)}^2}{1}=1$   .....  .....  .....  .....(2)

Comparing equations (1) and (2) gives

  $\left(h,k\right)=\left(2,0\right)$

Also, $a=2$ and $b=1$ . Since $a>b$ . So $x-$ axis is major axis.

The graph of the equation is -

  

Therefore, the correct graph of the given equation $\frac{{\left(x-2\right)}^2}{4}+y^2=1$ is option (g).