Point A and B are in the first quadrant,point O is the origin. If the slope of OA is 1,slope of OB is 7 and OA=OB,Then slope of AB is:

A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is-

A line is drawn through the point ( 1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is

Let, y = x line is median of the triangle OAB where O is origin. Equation ax^(2) +2hxy +by^(2) = 0,a,h,b in N , represents combined equation of OA and OB. A and B lie on the ordinate x = 3 . If slope of OA is twice the slope of OB, then greatest possible value of a +2h +b is

OABCDE is a regular hexagon of side 2 units in the XY-plane in the first quadrant. O being the origin and OA taken along the x-axis. A point P is taken on a line parallel to the z-axis through the centre of the hexagon at a distance of 3 unit from O in the positive Z direction. Then find vector AP.

In the given figure, OABC is a rectangle. Slope of OB is

Fill in the blanks A tangent from an external point A' touches the circle with centre O is B. If OB = 5cm, OA = 13 cm, then the length of AB is_______.

A man observes that when he moves up a distance c metres on a slope, the angle of depression of a point on the horizontal plane from the base of the slope is 30^0, and when he moves up further a distance c metres, the angle of depression of that point is 45^0dot The angle of inclination of the slope with the horizontal is.

A variable line L is drawn through O (0,0) to meet the lines L 1 ​ :y−x−10=0 and L 2 ​ :y−x−20=0 at the points A and B respectively. A point P is taken on L such that OP 2 ​ = OA 1 ​ + OB 1 ​ and P,A,B lies on same side of origin O. The locus of P is

If the point (2,3),(1,1) , and (x ,3x) are collinear, then find the value of x ,using slope method.

Find the equation of the line Passing through the point (-4, 3) with slope 1/2 .