Find the equation of the circle passing through the points (2, 3) | Filo
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Class 11

Math

3D Geometry

Conic Sections

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Find the equation of the circle passing through the points and and whose centre is on the line

Solution: Let the equation of circle be 

       .....(1)

where is center and is the radius.


Since, the circle passes through , so it satisfies eqn (1)



     .....(2)

Since, the circle passes through , so it satisfies eqn (1)



     .....(3)

Subtracting eqn (3) from eqn (2), we get

      ....(4)

Given center lies on the line

Since, center satisfies this equation.

       ....(5)

Solving eqn (4) and (5), we get



Put this value in (2), we get



Substituting these values in (1),



which is the equation of required circle.
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