Question

Find the equation of the circle which pass through the origin and points of intersection of circles x2 + y2 = 4 and line x + y = 2​

Answer 1

SOLUTION

TO DETERMINE

The equation of the circle which pass through the origin and points of intersection of circles x² + y² = 4 and line x + y = 2

EVALUATION

Here the circle passes through the points of intersection of circles x² + y² = 4 and line x + y = 2

Let the required equation of the circle is

( x² + y² - 4 ) + k ( x + y - 2) = 0

Now the above circle passes through the point ( 0,0)

( 0² + 0² - 4 ) + k ( 0 + 0 - 2) = 0

$\implies \sf{ - 4 - 2k = 0}$

$\implies \sf{ - 2k = 4}$

$\implies \sf{ k = - 2}$

Hence the required equation of the circle is

$\sf{ ({x}^{2} + {y}^{2} - 4) - 2(x + y - 2) = 0 }$

$\implies\sf{ {x}^{2} + {y}^{2} - 4 - 2x - 2 y + 4 = 0 }$

$\implies\sf{ {x}^{2} + {y}^{2} - 2x - 2 y = 0 }$

FINAL ANSWER

The required equation of the circle is

$\boxed{\sf{ \: \: {x}^{2} + {y}^{2} - 2x - 2 y = 0 } \: \: }$

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