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Finds out the center & radius of each of the following circles & sketch the graph of the circle.
a) x2+ y 2 = 1
b) x2+ ( y - 3)2 = 4
Solution
In all of these all that we actuallyhave to do is compare the equation to the standard form and recognizes the radius & center. Once that is done determine the four points talked about above and sketch in the circle.
x2+ y 2 = 1
In this case it's just x & y squared by them. The only way which we could have it is to have both h & k be zero. Thus the center & radius is,
center = (0, 0) radius =√1 = 1
Don't forget that the radius is the square root of the number on the other side of the equal sign. Following is a sketch of this circle.
L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12 R.H.S =c
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