A straight line through the origin O meets the parallel lines 4x+2y=9 and 2x+y+6=0 at 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 the point (2, 2) intersects the lines sqrt3 x + y = 0 and sqrt3 x - y = 0 at the points A and B. The equation of AB so that the triangle OAB is equilateral, where O is the origin.

C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangent at any point P on this hyperbola meet the straight lines b x-a y=0 and b x+a y=0 at points Qa n dR , respectively. Then prove that C QdotC R=a^2+b^2dot

The line y=(3x)/4 meets the lines x-y=0 and 2x-y=0 at points Aa n dB , respectively. If P on the line y=(3x)/4 satisfies the condition P AdotP B=25 , then the number of possible coordinates of P is____

A straight line passes through the point of Intersection of the lines x- 2y - 2 = 0 and 2x - by - 6= 0 and the origin, then the set of values of 'b' for which the acute angle between this line and y=0 is less than 45^@ is

Find the equation of a straight line through the point of intersection of the lines 8x+3y=18, 4x+5y=9 and bisecting the line segment joining the points (5, -4) and(-7, 6) .

Find the equation of the line through the point of intersection of the lines 2x+y-5=0 and x+y-3=0 and bisecting the line segment joining the points (3,-2) and (-5,6).

Find the equation of a straight line through the intersection of lines 3x+2y=10 and 5x-6y=2 and perpendicular to the line 4x-7y+13=0 .