Question

The equation of a circle is:(x + 2)2 = (y-2) = 13.There are two values of such that (0.]) is on the circle.Find both of those values. If necessary, round to the nearest tenth:The smaller value of j isThe larger value ofj isBlank 1:Blank 2:

Answer 1

the write out the equation of the circle given

$(x+2)^2+(y-2)^2=13$

Given the coordinate (0, j), we will find the values of j as shown below

$\begin{gathered} \text{Given coordinate} \\ (0,j) \\ x=0, \\ y=j \\ \text{substitute 0 and j for x and y in the equation of circle given} \end{gathered}$$\begin{gathered} (0+2)^2+(j-2)^2=13 \\ 2^2+(j-2)(j-2)=13 \\ 4+j^2-2j-2j+4=13 \\ j^2-4j+4+4-13=0 \\ j^2-4j-5=0 \end{gathered}$$\begin{gathered} j^2-5j+j-5=0 \\ j(j-5)+1(j-5)=0 \\ (j-5)(j+1)=0 \\ j-5=0,or,j+1=0 \\ j=5,or,j=-1 \end{gathered}$

Hence, the smaller value of j is -1, and the larger value of j is 5