Question

What is the approximate radius of the circle whose equation is ${(x - \sqrt 3 )^2} + {(y + 2)^2} = 11$
 A.$1.71$
B. $2.33$
C. $3.32$
D. $3.85$
E. $4.27$

Answer 1

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 ${(x - h)^2} + {(y - k)^2} = {r^2}$ . Comparing the given equation from the general equation.

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