Question 1158733
Given circle A with the equation

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

a) show that the circle passes through point ({{{0}}},{{{1}}})
plug in the coordinates of the given point

{{{ (0+2)^2+1^2=5}}}
{{{ 4+1=5}}}
{{{ 5=5}}}->true

so,  the circle passes through point ({{{0}}},{{{1}}})


b) state the coordinate of two other points that lie on the circle
{{{ (x+2)^2+y^2=5}}} compare to {{{ (x-h)^2+(y-k)^2=r^2}}}

=>{{{h=-2}}} and {{{k=0}}}=> the center is at point ({{{-2}}},{{{0}}})

{{{ (x+2)^2+y^2=5}}}  find {{{y}}} when {{{x=-2}}} 
{{{ (-2+2)^2+y^2=5}}} 
{{{ 0^2+y^2=5}}} 
{{{ y=sqrt(5)}}} 
{{{ y=2.24}}}  ->point ({{{-2}}},{{{2.24}}})


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(-2,0,.12),locate(-2,0.5,C(-2,0)),
circle(0,1,.12),locate(0,1,p(0,1)),
circle(-2,2.24,.12),locate(-2,2.24,p(-2,2.24)),
 graph( 600, 600, -10, 10, -10, 10,-sqrt(5-(x+2)^2) ,sqrt(5-(x+2)^2))) }}} 


c) write equation of circle A’; the image of circle A after a translation of {{{3 }}}units to the right and {{{1}}} unit up

The center of the given circle is at the ({{{-2}}},{{{0}}}). The translated center will be shifted {{{3}}} units to the right and {{{1}}} units up, placing it at (1,1). The circle has a radius of {{{5}}}. The equation will be: 

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

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(-2,0,.12),locate(-2,0.5,C(-2,0)),
circle(1,1,.12),locate(1,1,C(1,1)),
 graph( 600, 600, -10, 10, -10, 10,-sqrt(5-(x-1)^2)+1 ,sqrt(5-(x-1)^2)+1,
-sqrt(5-(x+2)^2) ,sqrt(5-(x+2)^2))) }}}

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.

{{{V=B*h}}}

{{{V=r^2*pi*h}}}......{{{r=5}}},{{{h=10}}}

{{{V=5^2*pi*10}}}
{{{V=250*pi}}}
{{{V=785.4}}}