SOLUTION: Given circle A with the equation (x+2)^2+y^2=5 a)show that the circle passes through point (0,1) b)state the coordinate of two other points that lie on the circle c)write equati

Algebra ->  Circles -> SOLUTION: Given circle A with the equation (x+2)^2+y^2=5 a)show that the circle passes through point (0,1) b)state the coordinate of two other points that lie on the circle c)write equati      Log On


   

Question 1158733: Given circle A with the equation (x+2)^2+y^2=5
a)show that the circle passes through point (0,1)
b)state the coordinate of two other points that lie on the circle
c)write equation of circle A’; the image of circle A after a translation of 3 units to the right and 1 unit up
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.
https://docs.google.com/document/d/140wt6R6O8qIPOvtNwDzxksQUaAwIwTow__7Rgf3nKio/edit
Thank you very much!
Found 3 solutions by josgarithmetic, Edwin McCravy, MathLover1:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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Given circle A with the equation (x+2)^2+y^2=5
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a)show that the circle passes through point (0,1)
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Make the substitution, x is 0, y is 1, and find if it makes the equation true or false.


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b)state the coordinate of two other points that lie on the circle
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Pick a value for one variable and solve for the other variable. You can find as many points as you want.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Given circle A with the equation
%28x%2B2%29%5E2%2By%5E2=5
%28x%2B2%29%5E2%2B%28y-0%29%5E2=5 
That circle has center (-2,0) and radius √5

a)show that the circle passes through point (0,1)
%28x%2B2%29%5E2%2By%5E2=5
%280%2B2%29%5E2%2B1%5E2=5
2%5E2%2B1=5
4%2B1=5
5=5
That is true so it proves that it passes through that point.


b)state the coordinate of two other points that lie on the circle
Pick any of those marked.  Substitute them as I did above with (0,1)

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

%28x%2B2%29%5E2%2By%5E2=5

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

%28%28x-3%29%2B2%29%5E2%2B%28y-1%29%5E2=5

%28x-1%29%5E2%2B%28y-1%29%5E2=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:
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=expr%281%2F3%29pi%2Ar%5E2h

Substitute r=√5, h=10.

Edwin

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Given circle A with the equation
+%28x%2B2%29%5E2%2By%5E2=5
a) show that the circle passes through point (0,1)
plug in the coordinates of the given point
+%280%2B2%29%5E2%2B1%5E2=5
+4%2B1=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
+%28x%2B2%29%5E2%2By%5E2=5 compare to +%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2
=>h=-2 and k=0=> the center is at point (-2,0)
+%28x%2B2%29%5E2%2By%5E2=5 find y when x=-2
+%28-2%2B2%29%5E2%2By%5E2=5
+0%5E2%2By%5E2=5
+y=sqrt%285%29
+y=2.24 ->point (-2,2.24)



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:
+%28x-1%29%5E2%2B%28y-1%29%5E2=5

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%2Ah
V=r%5E2%2Api%2Ah......r=5,h=10
V=5%5E2%2Api%2A10
V=250%2Api
V=785.4