If `L:x+y=(1)/(2)` intersects `x^(2)+y^(2)=1` at 2 points A & B .Then joint equation of line passing through origin & points A and B is

The equation of line passing through points A(2,1) and B(1,2) is ....

The line 3x+6y=k intersects the curve 2x^(2)+3y^(2)=1 at points A and B .The circle on AB as diameter passes through the origin. Then the value of k^(2) is

A line L passing through the point (2,1) intersects the curve 4x^(2)+y^(2)-x+4y-2=0 at the point A and B .If the lines joining the origin and the points A,B are such that the coordinate axes are the bisectors between them,then find the equation of line L.

If the line pass through the point(-3,-5) and intersect the ellipse x^2/4+y^2/9=1 at a point A and B . Then the locus of mid point of line joining A and B is

Line 3x + by = k intersect the curve 2x^2 + 3y^2 + 2xy=1 at points A and B. Thecircle on AB as diameter passes through origin,then sum of all possible values of 'k' is

Let a and b be two non -zero reals such that aneb . Then the equation of the line passing through origin and point of intersection of (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 is

If the lines L_(1):(x-1)/(3)=(y-lambda)/(1)=(z-3)/(2) and L_(2):(x-3)/(1)=(y-1)/(2)=(z-2)/(3) are coplanar, then the equation of the plane passing through the point of intersection of L_(1)&L_(2) which is at a maximum distance from the origin is

The joint equation of lines passing through the origin and perpendicular to lines represented by x^(2)+xy-y^(2)=0 is

Straight lines x-y=7 and x+4y=2 intersect at B. Point A and C are so chosen on these two lines such that AB=AC. The equation of line AC passing through (2,-7) is

Joint equation of lines passing through the origin, and parallel to the lines y-m_(1)x+c_(1) and y=m_(1)x+c_(2) , is