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Find the co-ordinates of a point p on line x + y--13, nearest to the circle x2 + y2 + 4x + 6y-5-(B) (- 15, 2) |
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Answer» The line through the nearest point must pass through center of circle and must be perpendicular to given line. Therefore, equation of line perpendicular to x+y+13=0 will be y-x+λ =0. It will be passing through center of circle which is (-4/2, -6/2) = ( -2,-3) So, (-3)-(-2)+λ=0 which gives λ= 1.Hence , equation of line will be y-x+1=0. Now, intersecting point of x+y+13=0 and y-x+1=0 will give the required point.Solving for x and y , x=-6 and y=-7So, the point is (-6,-7). |
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