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If the tangent at point P on the circle x^2+y^2+6x+6y-2=0 meet the straight line 5x-2y+6=0 at he point Q on the y axis then length ofPQis

If the tangent at point P on the circle x^2+y^2+6x+6y-2=0 meet the straight line 5x-2y+6=0 at he point Q on the y axis then length ofPQis
 

Grade:11

1 Answers

s sai suryateja
26 Points
5 years ago
Dear rajesh, 
the tangent to the circle which intersect y-axis at (0,3) i.e. point of intersection of the tangent and line 5x-2y+6=0
the tangent to the circle x2+y2+6x+6y-2=0 can be written as xx1+yy1+3(y+y1)+3(x+x1)-2=0
(0,3) satisfies the above equation of tangent
so the equation of tangent is 3x+6y+7=0
the formula of the length of tangent is (x12+y12+2gx1+2fy1+c)1/2
length of the tangent from the point is (02+32+0+18-2)1/2=5
hence the length of the tangent is 5

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