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  • Help me please, If y + 3x = 0 is the equation of a chord of the circle, x2 + y2 - 30x = 0, then the equation of the circle with this chord as diameter is :

 If y + 3x = 0 is the equation of a chord of the circle, x2 + y2 - 30x = 0, then the equation of the circle with this chord as diameter is :

  • Option 1)

    x^{2}+y^{2}+3x+9y=0

  • Option 2)

    x^{2}+y^{2}-3x+9y=0

  • Option 3)

    x^{2}+y^{2}-3x-9y=0

  • Option 4)

    x^{2}+y^{2}+3x-9y=0

 

Answers (1)

best_answer

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.

 

 given that y+3x=0;

y=-3x

x^{2}+y^{2}-30x=0

10x^{2}-30x=0  \Rightarrow x=0,3

Hence y=0, -9

In diametric form

\left ( x-3 \right )\left ( x-0 \right )+\left ( y+9 \right )\left ( y-0 \right )=0

x^{2}+y^{2}-3x+9y=0


Option 1)

x^{2}+y^{2}+3x+9y=0

Incorrect option

Option 2)

x^{2}+y^{2}-3x+9y=0

Correct option

Option 3)

x^{2}+y^{2}-3x-9y=0

Incorrect option

Option 4)

x^{2}+y^{2}+3x-9y=0

Incorrect option

Posted by

prateek

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