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Find the length of the chord of contact ...

Find the length of the chord of contact with respect to the point on the director circle of circle `x^2+y^2+2a x-2b y+a^2-b^2=0` .

Text Solution

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We have circle `S_(1)-=(x+a)^(2)+(y-b)^(2)=2b^(2)`
Equation of dirctor circle `S_(2)-=(x+a)^(2)+(y-b)^(2)=4b^(2)`.

Tangents PQ and PR are drawn to circle `S_(1)=0` from a point P on the director circle `S_(2)=0`.
So, QR is the chord of contact.
In the figure, PQCR is a square.
`:. QR=CP=` Radius of director circle `=2b`
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