A straight line through the origin o meets the parallel lines `4x+2y=9` and `2x+y+6=0` at the points `P` and `Q` respectively.Then the point o divides the segment `PQ` in the ratio-

A straight line through the origin 'O' meets the parallel lines 4x +2y= 9 and 2x +y=-6 at points P and Q respectively. Then the point 'O' divides the segment PQ in the ratio

A straight line through origin O meets the lines 3y=10-4x and 8x+6y+5=0 at point A and B respectively. Then , O divides the Segment AB in the ratio.

A straight line L through the origin meets the lines x + y = 1 and x + y = 3 at P and Q respectively. Through P and Q two straight lines L_1 , and L_2 are drawn, parallel to 2x-y- 5 and 3x +y 5 respectively. Lines L_1 and L_2 intersect at R. Locus of R, as L varies, is

A straight line through the point A (-2,-3) cuts the line x+3y=9 and x+y+1=0 at B and C respectively. If AB.AC =20 then equation of the possible line is

The straight line passing through the point of intersection of the straight line x+2y-10=0 and 2x+y+5=0 is

A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, 5) is the mid-point of PQ, then find the coordinates of P and Q.

A variable line L drawn through O(0,0) to meet line l1: y-x-10=0 and L2:y-x-20=0 at the point A and B respectively then locus of point p is ' such that (OP)^(2) = OA . OB,

A line intersects the Y- axis and X-axis at the points P and Q, respectively. If (2,-5) is the mid- point of PQ, then the coordinates of P and Q are, respectively.

Comprehension (Q.6 to 8) A line is drawn through the point P(-1,2) meets the hyperbola x y=c^2 at the points A and B (Points A and B lie on the same side of P) and Q is a point on the lien segment AB. If the point Q is choosen such that PQ, PQ and PB are inAP, then locus of point Q is x+y(1+2x) (b) x=y(1+x) 2x=y(1+2x) (d) 2x=y(1+x)

The tangent drawn to the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 , at point P in the first quadrant whose abscissa is 5, meets the lines 3x-4y=0 and 3x+4y=0 at Q and R respectively. If O is the origin, then the area of triangle OQR is (in square units)