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Question

If the length of the tangent from (2,5) to the circle x2+y25x+4y+k=0 is 37, then find k.

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Solution

Center of circle =(52,2)

Radius of circle =r=254+4k

As tangent is perpendicular to the radius, we apply Pythagoras theorem (see the figure)

AO2=AP2+PO2

14+49=r2+37

1974=254+4k+37

k=13

1182364_1436036_ans_56bcd48ecb2841fab15bdee4884579ea.png

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