Find a and b if te equations a x - 3y + 6 = 0 and 2x + b y - 9 = 0 represent the same straight line.

If 3x-by+2=0 and 9x+3y+a=0 represent the same straight line, find the values of a and b.

A person standing at the junction (crossing) of two straight paths represented by the equations 2x -3y + 4 = 0 and 3x + 4y -5 = 0 wants to reach the path whose equation is 6x -7y + 8 = 0 in the least time. Find equation of the path that he should follow.

A person standing at the junction (crossing) of two straight paths represented by the equations : 2x -3y -4 =0 and 3x + 4y -5 = 0, wants to reach the path whose equation is 6x - 7y + 8 = 0 in the least time. Find the equation of the path that he should follow.

The equation 3ax^2+9xy+(a^2-2)y^2=0 represents two perpendicular straight lines for

For what value of lambda does the equation 12x^2-10xy+2y^2+11x-5y+lambda=0 represent a pair of straight lines ? Find their equations and the angle between them.

If ax-2y-1=0 and 6x-4y+b=0 represent the same line, find the values of a and b.

Find the equations of the line through the intersection of 2x - 3y + 4 = 0 and 3x + 4y - 5= 0 and perpendicular to 6x-7y +c = 0

Find the acute angles between the st. lines : y-3x-5=0 and 3y -x +6= 0 .

Show that the lines 2x + 3y - 8 = 0 , x - 5y + 9 = 0 and 3x + 4y - 11 = 0 are concurrent.

Consider the straight lines x + 2y + 4 = 0 and 4x+ 2y - 1 = 0 . The line 6x + 6y + 7 = 0 is