The intercept on the line y=x by the circle  x^{2}+y^{2}-2x=0\; is\; AB. Equation of the circle on AB as a diameter is

  • Option 1)

    x^{2}+y^{2}+x+y=0

  • Option 2)

    x^{2}+y^{2}-x+y=0

  • Option 3)

    x^{2}+y^{2}-x-y=0

  • Option 4)

    x^{2}+y^{2}+x-y=0

 

Answers (1)

As we learnt in

Equation of a circle in diametric form -

\left ( x-x_{1} \right )\left ( x-x_{2} \right )+\left ( y-y_{1} \right )\left ( y-y_{2} \right )= 0

 

- wherein

Where A\left ( x_{1},y_{1} \right )\, and \:B \left ( x_{2},y_{2} \right ) are the two diametric ends.

 

 Equation of circle is 

x^{2}+y^{2}-2x=0

Since line AB is y = x, we find point of intersection

x^{2}+x^{2}-2x=0

=> x=0\: or\: x=1

Thus y = 0 or y = 1 

equation in diametric form

(x-0) (x-1)+(y-0)(y-1)=0

x^{2}+y^{2}-x-y=0


Option 1)

x^{2}+y^{2}+x+y=0

Incorrect option    

Option 2)

x^{2}+y^{2}-x+y=0

Incorrect option    

Option 3)

x^{2}+y^{2}-x-y=0

Correct option

Option 4)

x^{2}+y^{2}+x-y=0

Incorrect option    

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