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If the chord of contact of tangents from a point `P`to a given circle passes through `Q ,`then the circle on `P Q`as diameter.cuts the given circle orthogonallytouches the given circle externallytouches the given circle internallynone of theseA. cuts the given circle orthogonallyB. touches the given circle externallyC. touches the given circle internallyD. none of these |
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Answer» Correct Answer - A Let `P(x_(1), y_(1))` and `Q(x_(2), y_(2))` be the given points and `x^(2)+y^(2)=a^(2)` be the circle. The chord of contact of tangents drawn from `P(x_(1), y_(1))` to `x^(2)+y^(2)=a^(2)` is `x x_(1)+y y_(1)=a^(2)` If it passes through `Q(x_(2), y_(2))`, then `x_(1) x_(2)+y_(1)y_(2)=a^(2) " " ...(i)` The equation of the circle on PQ as diameter is `(x-x_(1))(x-x_(2))+(y-y_(1))(y-y_(2))=0` `rArr x^(2)+y^(2)-x(x_(1)+x_(2))-y(y_(1)+y_(2))+x_(1)x_(2)+y_(1)y_(2)=0` This circle will cut the given circle orthogonally, if `0(x_(1)+x_(2))+0(y_(1)+y_(2))=a^(2)+x_(1)x_(2)+y_(1)y_(2)` `rArr x_(1)x_(2)+y_(1)y_(2)=a^(2)=0`, which is true. [Using (i)] |
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