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  • Find the length of the chord intercepted by the circle x^2+y^2-6x+8y-5=0 on the line 2x-y=5.

Find the length of the chord intercepted by the circle x^2+y^2-6x+8y-5=0 on the line 2x-y=5.

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The given line is  2x-y-5=0
and the given circle is x^2+y^2-6x+8y-5=0
Its center is C(3,-4) and radius = sqrt9+16+5=sqrt30.
Let d be the perpendcular distance from C(3,-4) on the line (i), then 
d=frac|2 imes3-(-4)-5|sqrt2^2+(-1^2)=frac5sqrt5=sqrt5
We see that d<r,so the line (i) and circle (ii) intersect in two points.
Therefore The length of the chord intercepted=2sqrtr^2-d^2=2sqrt30-5=10

Posted by

Deependra Verma

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