Let the eq of circle be
x
2
+y
2
+2gx+2βy+c=0
now, x intercept = 2
g
2
−c
But circle touches x axis ∴ x intercept = 0
∴2
g
2
−c
=0∴g
2
=c
∴eq
n
become x
2
+y
2
+3gx+2βy+g
2
=0
Now circle passes through (3, 0) and (1, 4)
∴(3)
2
+(0)
2
+2g(3)+0+g
2
=0
9+6g+g
2
=0
∴g=−3
Also (1)
2
+(4)
2
+2(−3)(1)+2β(4)+9=0
∴1+16−6+8β+9=0
∴20+8β=0 ∴β=
2
5
Hence eq
n
of circle is
x
2
+y
2
−6x−5y+9=
U would measure it with the teaspoon and the 1/6 teaspoon
you would need 2 use the 1/2 teaspoon 4 times to get 2 teaspoons and the `1/6 teaspoon 4 times to get 2/3.
1/6+1/6=2/6*2=4/6 =2/3
hope this helps
Let w represent width;
Length 5/2+2w
Perimeter=2(l+w)
P=2(5/2+w+w)
P=2(5/2+2w)
P=2*5/2+2*2w)
P=5+4w