SOLUTION: write the equation of the circle satisfying the given condition.
Having a radius of {{{ sqrt( 85 ) }}} and passing through (5,9) and (1,-7)
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Question 969254: write the equation of the circle satisfying the given condition.
Having a radius of and passing through (5,9) and (1,-7)
Answer by anand429(138) (Show Source): You can put this solution on YOUR website!
Slope of line (or say chord) joining the two points on circumference
=
=
=
So, slope of perpendicular bisector of this chord
= (For perpendicular lines, product of slopes = -1)
So let the equation of perpendicular bisector of this chord(which shall pass through center of circle) be given by
-(i) (slope-intercept form of a line)
Now mid point of the chord is given by
,
i.e.(3,1)
Since this should lie on the line given by eqn (i)above,
So,
i.e.
So eqn of perpendicular bisector passing through center becomes
or,
Taking center as (7-4y,y), Its distance from both circumferential points is given by radii
So, for point (5,9)
(Using Distance formula)
i.e.
i.e.
So,
There will be two required circles with centers at (7,0) and (-1,2) and radius sqrt(85)
So, the equation of cirles be given by:
and
Simplify, if you want.
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