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  • from 3,4 chords are drawn to circle x2+y2-4x=0 the locus of mid points of the chord is

from 3,4 chords are drawn to circle x2+y2-4x=0 the locus of mid points of the chord is

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equation can be rewritten as  \left ( x-2 \right )^2 + y^2 =4

let the mid point of chord be P(a,b)

center of circle is  C(2,0)

let R(3,4)

PCR form a right angled triangle, making right angle at \angle CPR.

So \left ( 3-2 \right )^2+\left ( 4-0 \right )^2=\left ( a-2 \right )^2+\left ( b \right )^2+\left ( a-3 \right )^2+\left ( b-4 \right )^2

=\left ( a^2+b^2 \right )-5a-4b+6=0

=\left ( a-\frac{5}{2} \right )^2+\left ( b-2 \right )^2=\frac{17}{4}

=\left ( x-\frac{5}{2} \right )^2+\left ( y-2 \right )^2=\frac{17}{4}

Posted by

Randheer Kumar Gautam

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