Homework Soursehelp me please 1 xaxis have 2 points 20 and 80 its center in
help me please
1) x-axis have 2 points (2,0) and (8,0) its center in 1st quadrant , find a) center ,and radius of circle b) find the equation of the circle?
Solution
Solution:
As we know that general equation of circle is
(x-h)2+(y-k)2= r2 ...1
Where h and k is coordinates of center and r is radius of that circle
x and y are any arbitrary points on that circle
Now
it is given that (2, 0 ) and (8,0) lie on that given circle
therefore plug x = 2 and y = 0 in equation first
(2-h)2 + (0-k)2 = r2 ... (A)
similerly for point (8,0)
(8-h)2 + (0-k)2 = r2 ..,. B
Now substract equation A from B
ie (B) - (A )
(8-h)2 + (0-k)2 - (2-h)2 (0-k)2 = r2- r2
(8-h)2 - (2-h)2 = 0
64 +h2 -16h -4 -h2+4h = 0
-12h = -60
h = 5
Now ,
Plug h = 5 in equation A and B
we get same result
9 + (k)2 = r2
9 + (k)2 = r2
that means
value of k can be taken aribtrary positive ( since center lie in 1st quadrant )
that must satisfy
this euation
(x-5)2+(y-k)2= r2
therefore
(a)
center is ( 5,k)
radius r
( k is any aribitray positive value )
(b)
equation of circle
(x-5)2+(y-k)2= r2
Example
let\'s take k = 1
then r2 = 32 + 12
r = 10
