Posted by Anonymous on .
hich is the equation of a circle with diameter AB with A(5,4) and B(1,4)?
possible answers;
(x5)^2+(y4)^2=10
(x+5)^2+(y+4)^2=100
(x2)^2+y^2=25
(x+2)^2+y^2=5
Not sure

geometry 
MathMate,
Standard equation of a circle with a radius of r and centre (x0,y0) is:
(xx0)²+(yy0)²=r²
Centre of circle:
((51)/2, (4+(4))/2)=(2,0)
Out of the four choices, there is only one that has a centre positioned at (2,0).
(hint: refer to the standard equation of the circle)
Radius, r:
Radius of circle = distance from centre to circumference
r = sqrt((52)^2+(40)^2)=5
This confirms the choice above.
(hint: refer to the standard equation of the circle) 
geometry 
Anonymous,
This is what I have but not sure if right
(x(2)^2+(y3)^2=5^2
(x+2)^2+(y3)^2=25 
geometry 
MathMate,
I do not have the same answer as you.
If AB is the diameter, the centre is located at the midpoint between A and B.
The midpoint between A and B is
((Xa+Xb)/2, (Ya+Yb)/2)=(2,0)
I do not know how you got 2 and 3 for the centre of the circle. Can you explain? 
geometry 
lilman,
I was looking at wrong problem for this one a I got (x+5)^2+(y+4)^2=100

geometry 
MathMate,
Your answer is not correct.
Please explain how you got
(x+5)^2+(y+4)^2=100 as your answer.
Hint:
Centre of circle is at:
((51)/2, (4+(4))/2)=(2,0) 
geometry 
lilman,
(x+2)^2+y^2=5

geometry 
MathMate,
1. Centre is at (2,0)
but
(x+2)^2+y^2=5
has a centre at (2,0)
2. radius is 5, so the right hand side should be 5^2=25. 
geometry 
lilman,
Now I'm definitely lost would you mind explaining the whole process so I might understand?

geometry 
MathMate,
I guess you have not read this on Sunday:
Standard equation of a circle with a radius of r and centre (x0,y0) is:
(xx0)²+(yy0)²=r²
Centre of circle:
((51)/2, (4+(4))/2)=(2,0)
Out of the four choices, there is only one that has a centre positioned at (2,0).
(hint: refer to the standard equation of the circle)
Radius, r:
Radius of circle = distance from centre to circumference
r = sqrt((52)^2+(40)^2)=5
This confirms the choice above.
(hint: refer to the standard equation of the circle) 
geometry 
lilman,
Okay, 9+16=25
so would my answer be (x2)^2+(y^2)=25
I thiught you had to take the square rt of 25 
geometry 
MathMate,
Yep, you got it, congrats!
I hope you understand how it works.
If not, feel free to post. 
geometry 
cupcake,
The answer is (x2)2+y2=25 i just took it on my quiz and all the other answers are wrong!!! so i got it wrong at first!! but this is the correct one!