Q

# Can someone explain - Two-dimensional Coordinate Geometry - BITSAT

If y=$2x$ is a chord of the circle $x^{2}+y^{2}=10x,then$ the equation of the circle whose diameter is this chord is

• Option 1)

$x^{2}+y^{2}+2x+4y=0$

• Option 2)

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

• Option 3)

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

• Option 4)

None of these

96 Views

Family of circle -

$S+KL= 0$

- wherein

Equation of the family of circles passing through point of intersection $S=0 \, and\, line\, L=0$.

$(x^{2}+y^{2}-10x)+\lambda (2x-y)=0$ is a family of circle

Centre $\equiv \left ( 5-\lambda , \frac{\lambda }{2} \right )$

it lies on $y=2x$

$\therefore 10-2\lambda -\frac{\lambda }{2}=0$

$\Rightarrow \lambda =4$

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

Option 1)

$x^{2}+y^{2}+2x+4y=0$

This solution is incorrect

Option 2)

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

This solution is incorrect

Option 3)

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

This solution is correct

Option 4)

None of these

This solution is incorrect

Exams
Articles
Questions