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circles
Asked by ashwinikumar59 | 30 Apr, 2010, 03:21: PM Expert Answer

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

Answered by | 30 Apr, 2010, 05:35: PM
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