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Question

Equation of the circle passing through (2,3) and centre at the origin is _______ .


A

(x2)2+(y3)2=13

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B

x2+y2=13

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C

(x3)2+(y2)2=13

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D

x2y2=13

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Solution

The correct option is B

x2+y2=13


The formula for the equation of a circle is (xh)2+(yk)2=r2, where (h,k) represents the coordinates of the centre of the circle, and r represents the radius of the circle.

Given, centre = (0,0) and (2,3) is a point on the circle.

Then the radius 'r' of this circle is the distance between (2,3) and (0,0).

i.e. r2=(30)2+(20)2=13

Now, the equation of the circle is,

(x0)2+(y0)2=13

x2+y2=13


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