Let 
be the equation of a chord of the circle 
(in the closed half-plane 
) of diameter 10 passing through the origin. Let 
be another circle described on the given chord as its diameter. If the equation of the chord of the circle 
, which passes through the point 
and is farthest from the center of 
, is 
, then 
is equal to
Text Solution
Verified by ExpertsA
Circle 
has radius 5 and chord on line 
through origin.
Setting center at 
(in region 
), the chord endpoints are 
and 
by solving 
.
Circle 
has this chord as diameter, so center is at 
with radius 
.
The chord of 
through 
that is farthest from center is perpendicular to the radial direction from center to 
.
The radial direction is 
with normal direction 
.
The chord equation is 
, giving 
.
In form 
, we have 
and 
, so 
.
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