Question

match each graph with correct equation

$$\begin{gathered} \left(a\right){(x-3)}^2+{(y+3)}^2=9,\left(b\right){(x+1)}^2+{(y-2)}^2=4, \\ \left(c\right){(x-1)}^2+{(y+2)}^2=4,\left(d\right){(x+3)}^2+{(y-3)}^2=9 \end{gathered}$$

Short answer

The correctly matched equation of the given question is option (b)${(x+1)}^2+{(y-2)}^2=4$

Step-by-step solution

. Given information

The graph of the circle is given.

we need to match the graph with the correct equation.

. Plot the graph of option (a)x-32+(y+3)2=9

The standard form of equation is ${(x-h)}^2+{(y-k)}^2=r^2,where(h,k)isthecenterandristheradius$

so here given equation ${(x-3)}^2+{(y+3)}^2=9$ is in the form of standard form of the equation of a circle and then the radius is 3 and center is (3,-3) , the graph is given below

Step 3. Plot the graph of  option (b)x+12+y-22=4

${(x+1)}^2+{(y-2)}^2=4$

is the equation of a circle which is in the form of standard form of the equation of a circle , then radius is 2 and center is(-1, 2) here. Hence sketched graph of this equation is given below

Step 4. Sketch the graph of option (c)(x-1)2+(y+2)2=4

Given equation of a circle is${(x-1)}^2+{(y+2)}^2=4$ and this is similar to a standard form of the equation of a circle, then the center is (1,-2 ) and radius is 2. The plotted graph is given below

Step 5. Sketch the graph of option (d)x+32+(y-3)2=9

Here given equation is ${(x+3)}^2+{(y-3)}^2=9$

and compared to this to standard form of a circle the we get center is (-3, 3) and radius is 3. then the graph is given below

Step 6. Matching the correct equation

The plotted graph of the equation for each option and the exact match of the equation of the given question graph is option (b)${(x+1)}^2+{(y-2)}^2=4$