Q54 of 59 Page 178

State whether the statements are true or false.

The line moves in such a way that , where c is a constant. The locus of the foot of the perpendicular from the origin on the given line is x2 + y2 = c2.

We have equation of line

…(i)


Equation of line passing through the origin and perpendicular to the given line


…(ii)


Now, the foot of perpendicular from origin on the line (i) is the point of intersection of lines (i) and (ii).


So, to find its locus we have to eliminate the variable a and b.


Squaring and adding eq. (i) and (ii), we get








⇒ x2 + y2 = c2


Hence, the given statement is TRUE


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