Question

at them and then that in 'n (0 2. emewah of the followme equations represale with a walan rere radius (a) 10 (h) 1191 18 (a) ix'. '16 1 * Find the equation of the cinle which passes through (s) and is concentle with

Answer 1

`x^2+y^2+2x-4y=0`

Rewrite the equation in the standar form:

`(x-h)^2+(y-k)^2=r^2`

So:

`\begin{gathered} x^2+y^2+2x-4y=0 \\ x^2+y^2+2x-4y=(x+1)^2+(y-2)^2-5 \\ so\colon \\ (x+1)^2+(y-2)^2=5 \end{gathered}`

Since the circles are concentric they share the same center, therefore, for the other circle, the Center(h,k) is also:

`C(h,k)=(-1,2)`

Using the standard equation of the circle again:

`(x+1)^2+(y-2)^2=r^2`

We need to find the radius, however, we know one of the points of the circle, which is:

`(x1,y1)=(5,3)`

Evaluating the point into the equation:

`\begin{gathered} (5+1)^2+(3-2)^2=r^2 \\ 36+1=r^2 \\ 37=r^2 \end{gathered}`

Therefore, the equation is:

`(x+1)^2+(y-2)^2=37`