If `u=a_1x+b_1y+c_1=0,v=a_2x+b_2y+c_2=0,` and `(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2),` then the curve `u+k v=0` is (a)the same straight line `u` (b)different straight line (c)not a straight line (d)none of these

The angle between the two straight line of a pair of straight line x^2 - y^2 - 2y - 1 = 0 is

The locus of the point (sqrt(3h),sqrt(3k+2)) if it lies on the line x-y-1=0 is (a) straight line (b) a circle (c) a parabola (d) none of these

If the line (x/a)+(y/b)=1 moves in such a way that (1/(a^2))+(1/(b^2))=(1/(c^2)) , where c is a constant, prove that the foot of the perpendicular from the origin on the straight line describes the circle x^2+y^2=c^2dot

The equation x^2y^2-9y^2-6x^2y+54 y=0 represents (a) a pair of straight lines and a circle (b) a pair of straight lines and a parabola (c) a set of four straight lines forming a square (d) none of these

Determine the constant c such that the straight line joining the points (0,3) and (5-2) is a tangent to the curve y=(c )/(x+1) .

The straight line a_(1)x+b_(1)y+c_(1)=0 anda_(2)x+b_(2)y+c_(2)=0 are parallel to each other if -

If b_1. b_2=2(c_1+c_2) then at least one of the equation x^2+b_1x+c_1=0 and x^2+b_2x+c_2=0 has a) imaginary roots b) real roots c) purely imaginary roots d) none of these

The variable coefficients a, b in the equation of the straight line (x)/(a) + (y)/(b) = 1 are connected by the relation (1)/(a^(2)) + (1)/(b^(2)) = (1)/(c^(2)) where c is a fixed constant. Show that the locus of the foot of the perpendicular from the origin upon the line is a circle. Find the equation of the circle.

Equations (b-c)x+(c-a)y+(a-b)=and(b^(3)-c^(3))x+(c^(3)-a^(3))y+a^(3)-b^(3)=0 will represent the same straight line if -

If the two lines a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0 cut the co-ordinates axes in concyclic points. Prove that a_1a_2 = b_1b_2