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        the feet of perpendicular from the origin on a variable chord of the circle X2 + Y2 -2 X - 2y = 0 is  N.  if the variable chord makes an angle of 90 degree at the origin then the locus of N  has the equation....?
6 months ago

Dr Bhishma Hazarika
23 Points
							Let (a,b) is the foot of the perpendicular drawn on the variable chord of the circle from the origin.  So, Equation of the chord  $y-b=-a/b(x-a)$                                        or $ax+by={a}^2 +b^2$                                        or  $\frac{ax+by}{a^2+b^2 }=1$….....................(1)  Now hoogeneous form of the given circle by equation is     $x^2+y^2-2x\frac{ax+by}{a^2+b^2}-2y\frac{ax+by}{a^2+b^2}=0$    It will represent pair of st.lines. but by question chord makes 900 at the origin;               so  co-officiant of $x^2$+co-officiant of $y^2$ is zero     i.e

5 months ago
Dr Bhishma Hazarika
23 Points
							Continue from the first answer......  $(1-\frac{2a}{a^2+b^2})+(1-\frac{2b}{a^2+b^2})= 2(a^2+b^2)-2a-2b=0$  so locus of the foot of the perpendicular from the orogin is another circle   $2(x^2+y^2)-2x-2y=0$

5 months ago
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