If y = mx be the equation of a chord o...

If y = mx be the equation of a chord of a circle whose radius is a, the origin of coordinates being one extremity of the chord and the axis of x being a diameter of the circle, prove that the equation of a circle of which this chord is the diameter is ` (1 + m^(2)) ( x^(2) + y^(2)) - 2a (x + my) = 0`

AI Generated Solution

Similar Questions

Explore conceptually related problems

If y=mx be the equation of a chord of the circle prove that the circle of which this chord is the diameter is (1+m^(2))(x^(2)+y^(2))-2a(x+my)=0

y=2x is a chord of the circle x^(2)+y^(2)-10x=0, then the equation of a circle with this chord as diameter is

If y=2x is a chord of the circle x^(2)+y^(2)-10x=0, find the equation of a circle with this chord as diameter.

If y=2x is the chord of the circle x^(2)+y^(2)-4x=0, find the equation of the circle with this chord as diameter.

If y+3x=0 is the equation of a chord of the circle,x^(2)+y^(2)-30x=0, then the equation of the circle with this chord as diameter is:

The equation of a circle whose end the points of a diameter are (x_(1), y_(1)) and (x_(2),y_(2)) is

Determine equation of the circle whose diameter is the chord x+y=1 of the circle x^(2)+y^(2)=4

The probability of the diameter of a circle being the longest chord of he circle is :

The equation of the circle whose diameter is common chord to the circles