1thanx...
1.Find the eqn of straight line of the family (x+y)+k(2x-y+1) which is farthest from (1,-3).
(ans:: 15y-6x=7)
2.A line is drawn thru (0,0) intersecting the lines 2x+y-2=0 and x-2y+2=0 @ A and B. then the locus of mid pt of AB is________________.
(ans:: 2x2-3xy-2y2+x+3y=0)
3.If the line y=√3xcuts the curve x3+y3+3xy+5x2+3y2+4x+5y-1=0 at the points A,B,C then OA.OB.OC=_________________,
(ans:: (4/13)(3√3 -1) )
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2 Answers
111)the family of lines passes thru (-1/3,1/3) find equation of line perpendicular to line joining the two points and passing thru(-1/3,1/3).
2)assume unknown line to be y=mx find the points of intersections with given lines.assume mid point(h,k) and
22+m+22m-1=2h
2m2m-1+2m2+m=2k
on eliminating m you get required locus.
3)assume a genral point(rcos60°,rsin60°) and let it satisfy the curve you will get a cubic in r whose roots are the distances required find product of those roots.