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from a point p perpendicular pm and pn are drawn upon x and y axes respectively.if mn passes through a fixed point (a,b),then the locus of p?

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Please find below the solution to the asked query :



Let the point P be x1,y1As PM and PN are perpendicular on X-axis and Y-axis respectively.So,Coordinates of M are x1,0 and coordinates of N are 0,y1 .Equation of line MNy-0x-x1=y1-00-x1-x1 y=y1 x-x1As it passes through (a,b)-x1b=y1 a-x1-bx1=ay1-x1y1bx1+ay1-x1y1=0bx1+ay1=x1y1bx1x1y1+ay1x1y1=1ax1+by1=1Thus, Locus of P is ax+by=1
 
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