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Question: What is the approximate radius of the circle whose equation is \({(x - \sqrt 3 )^2} + {(y + 2)^2} = ...

What is the approximate radius of the circle whose equation is (x−3)2+(y+2)2=11{(x - \sqrt 3 )^2} + {(y + 2)^2} = 11
A.1.711.71
B. 2.332.33
C. 3.323.32
D. 3.853.85
E. 4.274.27

Explanation

Solution

Hint : A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. The general equation of circle (x−h)2+(y−k)2=r2{(x - h)^2} + {(y - k)^2} = {r^2} . Comparing the given equation from the general equation.

Complete step-by-step answer :
Given equation is (x−3)2+(y+2)2=11{(x - \sqrt 3 )^2} + {(y + 2)^2} = 11
Comparing the given equation from (x−h)2+(y−k)2=r2{(x - h)^2} + {(y - k)^2} = {r^2}
Comparing we get,
Therefore, (x−h)2=(x−3)2{(x - h)^2} = {(x - \sqrt 3 )^2}
And (y−k)2=y−(−2)2{(y - k)^2} = {\\{ y - ( - 2)\\} ^2}
And r2=11{r^{^2}} = 11 …. (I)
Further solving equation (I)
r2=11{r^2} = 11
Taking under root on both sides,
r=11r = \sqrt {11}
The appropriate radius of the circle is 11=3.316\sqrt {11} = 3.316
So, option (C) is correct.
So, the correct answer is “Option C”.

Note : Properties of circle:
I.The circles are said to be congruent if they have equal radii.
II.The diameter of a circle is the longest chord of a circle.
III.Equal chords of a circle subtend equal angles at the center.
IV.The radius drawn perpendicular to the chord bisects the chord.
V.Circles having different radii are similar.