Points out of
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To find out if a point is inside, on, or outside a circle, we need to substitute the ordered pair into the equation of the circle:
(x-xc)^2+(y-yc)^2=r^2
where (xc,yc) is the centre of the circle, and r=radius of the circle.
If the left-hand side [(x-xc)^2+(y-yc)^2] is less than r^2, then point (x,y) is INSIDE the circle. If the left-hand side is equal to r^2, the point is ON the circle.
Finally, if the left-hand side is greater than r^2, the point is OUTSIDE the circle.
For the given problem, we have xc=3, yc=0, or centre at (3,0), r=sqrt(49)=7
(x-xc)^2+(y-yc)^2=r^2 => (x-3)^2+y^2=7^2
A. (-1,1),
(x-3)^2+y^2=7^2 => (-1-3)^2+1^2=16+1=17 <49 [inside circle]
B. (10,0)
(x-3)^2+y^2=7^2 => (10-3)^2+0^2=49+0=49 [on circle]
C. (4,-8)
(x-3)^2+y^2=7^2 => (4-3)^2+(-8)^2=1+64=65 > 49 [outside circle]
(x-xc)^2+(y-yc)^2=r^2
where (xc,yc) is the centre of the circle, and r=radius of the circle.
If the left-hand side [(x-xc)^2+(y-yc)^2] is less than r^2, then point (x,y) is INSIDE the circle. If the left-hand side is equal to r^2, the point is ON the circle.
Finally, if the left-hand side is greater than r^2, the point is OUTSIDE the circle.
For the given problem, we have xc=3, yc=0, or centre at (3,0), r=sqrt(49)=7
(x-xc)^2+(y-yc)^2=r^2 => (x-3)^2+y^2=7^2
A. (-1,1),
(x-3)^2+y^2=7^2 => (-1-3)^2+1^2=16+1=17 <49 [inside circle]
B. (10,0)
(x-3)^2+y^2=7^2 => (10-3)^2+0^2=49+0=49 [on circle]
C. (4,-8)
(x-3)^2+y^2=7^2 => (4-3)^2+(-8)^2=1+64=65 > 49 [outside circle]
Answer:
To find the sum of a + b where a and b are rational number.
1. when a and b are natural numbers
just add them . for example a =3, b=8
then ,a + b = 11
2. When a and b are whole numbers,
simply add them . for example a= 0, b=8
a+ b = 0 + 8= 8
3. When a and b are integers
for example, a =-1 b=8,
a+ b= -1+ 8 =7,
a=-2, b= -8
a+ b= -2-8=-10
a= -6 , b=2
a+ b= -6 + 2= -4
a= 8, b= -2
a+ b= 8 +(-2) =6
I have written this because Rational number = [Integers{Whole number(Natural number)}]
now when a= Any fraction= and b = Any fraction=
now ,
Find L.C.M of q and v
= if q and v are Co-prime , just multiply them to find their L.C.M.
For example 14,9. LCM=14×9=126
Otherwise, Find factors of q and v . Then take out common factors first and then multiply the remaining with with common factors.For example
q=12 and v=18
12 =2×2×3
18=2×3×3
common factor =2,3
non common=2,3
L.C.M= 2×2×3×3=36
Suppose LCM of q and v = r
then ,
=
=
then ,
a + b=