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Find k if the length of the tangent segment from (8,-3) to the circle x2+y2−2x+ky−23=0 is √10 units. - Mathematics and Statistics

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Find k if the length of the tangent segment from (8,-3) to the circle ` x^2+y^2-2x+ky-23=0` is `sqrt10 ` units.

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Solution

Length of tangent from a point (x, y)

`PT=sqrt(x_1^2+y_1^2+2gx_1+2fy_1+c)`

Given that ` PT=sqrt10`

`10=8^2+(-3)^2-2(8)+k(-3)-23`

`10 = 64 +9 -16 - 3k - 23`

`24 - 3k = 0`

`3k = 24`

`k = 8`

Concept: Circle - Length of Tangent Segments to Circle
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