CBSE Class 11-science Answered

Circle of radius a and diameter on x axis.

y = mx is the chord.

The first point is origin for the chord at the other point y = mx, but this point is also on the circle,

so

x² + y² = a²

x² + m²x² = a²

x = ±a/(1 + m²)

For the circle with diameter as the chord, the center will be at (x/2, mx/2) since the two end points of the chord are (0,0) and (x. mx/2)

and radius², ((x/2)² + (mx/2)²) = ((x² + m²x²)/4) = a²/4 

Hence the equation of the circle,

(x - (a/(1 + m²))² + (y - a/(1 + m²))²  = a²/4

regards,

Team,

TopperLearning.

)² + y² = a²