Chapter 11, Problem 6CCSR

Solution

To find: The new equation of the circle $x^2+y^2=9$ when it is translated 1 unit up and two units to left.

The new equation of the circle $x^2+y^2=9$ when it is translated 1 unit up and two units to left is ${(x+2)}^2+{(y-1)}^2=9$ .

Given:

The equation of circle is $x^2+y^2=9$ .

It is translated 1 unit up and two units left.

Concept used:

The equation of circle with radius r and centre $\left(a,b\right)$ is

  ${(x-a)}^2+{(y-b)}^2=r^2$

Calculation:

Given the graph is translated two units to left and one unit to up. Previous center of circle was (0,0). Now translating two units left and one unit up the center is (-2,1) and the radius remain same 3.

Thus, the equation of new circle is

  $\begin{array}{}$ {(x-(-2))}^2+{(y-1)}^2=9$$ {(x+2)}^2+{(y-1)}^2=9$\end{array}$

After translating two units to left and one unit up the equation of new circle is ${(x+2)}^2+{(y-1)}^2=9$ option I is correct.