STRAIGHT lines

JEE Main Discussion Forum › Co-ordinate Geometry questions › STRAIGHT lines

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=âˆš3xcuts the curve x³+y³+3xy+5x²+3y²+4x+5y-1=0 at the points A,B,C then OA.OB.OC=_________________,
(ans:: (4/13)(3âˆš3 -1) )

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2 Answers

jeetopper jee ·2011-02-25 21:58:58

1)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(rcos60Â°,rsin60Â°) and let it satisfy the curve you will get a cubic in r whose roots are the distances required find product of those roots.