Let `(h , k)` be a fixed point, where `h >0,k > 0.` A straight line passing through this point cuts the positive direction of the coordinate axes at the point `Pa n dQ` . Find the minimum area of triangle `O P Q ,O` being the origin.

A straight line L with negative slope passes through the point (8, 2) and cuts the positive co-ordinate axes at points P and Q. Find the absolute minimum value of OP + OQ, as L varies, where O is the origin.

Find the equation of the straight line passing through the point (2,3) and through the point of intersection of the lines 2x-3y+7=0 and 7x+4y+2=0

A straight line L with negative slope passes through the point (8,2) and cuts the positive coordinates axes at points (8,2) and cuts the positive coordinates axes at points P and Q .As L varies the absolute minimum value of OP + OQ is (O is origin )

Find the direction cosines of the line passing through the points P(2,3,5), and Q(-1,2,4).

Find the equation of a straight line passing through the point of intersection of the lines : 3x +y-9 =0 and 4x + 3y-7=0 and perpendicular to the line 5x -4y + 1 =0.

Find the direction cosines of a line passing through the points (1,0,0) and (0,1,1).

A straight line drawn through the point P(2,3) and is incline at an angle of 30^0 with the x-axis. Find the coordinates of two points on it a distance 4 from P on either side of Pdot

If 3a + 2b + 6c = 0 the family of straight lines ax+by = c = 0 passes through a fixed point . Find the coordinates of fixed point .

A circle of constant radius a passes through the origin O and cuts the axes of coordinates at points P and Q . Then the equation of the locus of the foot of perpendicular from O to P Q is

If a ,\ b , c are in A.P., then the line a x+b y+c=0 passes through a fixed point. write the coordinates of that point.