Question 1158733
Given circle A with the equation 

{{{(x+2)^2+y^2=5}}}

{{{(x+2)^2+(y-0)^2=5}}}

<pre>That circle has center (-2,0) and radius √5</pre>
a)show that the circle passes through point (0,1)

{{{(x+2)^2+y^2=5}}}
{{{(0+2)^2+1^2=5}}}
{{{2^2+1=5}}}
{{{4+1=5}}}
{{{5=5}}}

That is true so it proves that it passes through that point.

{{{drawing(400,400,-5,2,-2.5,4.5, graph(400,400,-5,2,-2.5,4.5),
circle(-2,0,sqrt(5)),  circle(0,1,.05), locate(0,1,"(0,1)"),
circle(-4,1,.05),locate(-4,1,"(-4,1)"), circle(-1,2,.05),locate(-1.8,2,"(-1,2)"),
circle(-3,2,.05),locate(-3,2,"(-3,2)"), 
circle(-2,0,.05),locate(-2,.3,"(-2,0)"),
circle(-4,-1,.05),locate(-4,-1,"(-4,-1)"), circle(-1,-2,.05),locate(-1,-2,"(-1,-2)"),
circle(-3,-2,.05),locate(-3,-1.8,"(-3,-2)"),
circle(0,-1,.05),locate(0,-1,"(0,-1)"), circle(-1,2,.05),locate(-1.8,2,"(-1,2)"),
circle(-3,2,.05),locate(-3,2,"(-3,2)")    

 
   )}}}
 
</pre>b)state the coordinate of two other points that lie on the circle<pre>
Pick any of those marked.  Substitute them as I did above with (0,1)</pre>
c)write equation of circle A’; the image of circle A after a translation of 3 units to the right and 1 unit up<pre>
Take 

{{{(x+2)^2+y^2=5}}}

,replace x by x-3 and y by y-1:

{{{((x-3)+2)^2+(y-1)^2=5}}}

{{{(x-1)^2+(y-1)^2=5}}}

Which is a circle with center (1,1) and the same radius of course,
the circle on the right that is only partly shown:

{{{drawing(400,400,-5,2,-2.5,4.5, graph(400,400,-5,2,-2.5,4.5),
circle(-2,0,sqrt(5)),  circle(0,1,.05), locate(0,1,"(0,1)"),
circle(-4,1,.05),locate(-4,1,"(-4,1)"), circle(-1,2,.05),locate(-1.8,2,"(-1,2)"),
circle(-3,2,.05),locate(-3,2,"(-3,2)"), 
circle(-2,0,.05),locate(-2,.3,"(-2,0)"),
circle(-4,-1,.05),locate(-4,-1,"(-4,-1)"), circle(-1,-2,.05),locate(-1,-2,"(-1,-2)"),
circle(-3,-2,.05),locate(-3,-1.8,"(-3,-2)"),
circle(0,-1,.05),locate(0,-1,"(0,-1)"), circle(-1,2,.05),locate(-1.8,2,"(-1,2)"),
circle(-3,2,.05),locate(-3,2,"(-3,2)"),
circle(1,1,.05),locate(1,1,"(1,1)"),

circle(1,1,sqrt(5))    

 
   )}}}

</pre>d)If circle A is the base of a right circular cylinder with a height of 10, find the volume of the cylinder to the nearest tenth.<pre> 

{{{V=expr(1/3)pi*r^2h}}}

Substitute r=√5, h=10.

Edwin</pre>