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Q.

The point where the perpendicular from the point −5,7meets the line 3x+4y+12=0 is h,k then the value of  h2k+2 is

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answer is -1.

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Detailed Solution

If (h,k) is foot of the perpendicular of x1,y1 on the line ax+by+c=0 then h−x1a=k−y1b=−ax1+by1+ca2+b2Hence, h+53=k−74=−3−5+47+1232+42h+53=k−74=−2525h+53=k−74=−1Therefore,h+53=-1h+5=-3h=−8        And      k−74=−1k−7=−4k=3Hence,h2k+2=−823+2=−88 Therefore, h2k+2=−1
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