Show that the equation of the straight line joining the points (a,b) and (c,d) can be written as `(x-a)(y-d)=(x-c)(y-b)`.

Show that the equation of the straight line joining the points (x_(1),y_(1))and(x_(2),y_(2)) can be expressed in the form (x-x_(2))(y-y_(1))=(x-x_(1))(y-y_(2)) .

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) .

Show that the equation of the straight line throught (alpha,beta) and through the point of intersection of the lines a_(1)x+b_(1)y+c_(1)=0 anda_(2)x+b_(2)y+c_(2)=0 is (a_(1)x+b_(1)y+c_(1))/(a_(1)alpha+b_(1)beta+c_(1))=(a_(2)x+b_(2)y+c_(2))/(a_(2)alpha+b_(2)beta+c_(2))

The equation to the chord joining two points (x_1,y_1)a n d(x_2,y_2) on the rectangular hyperbola x y=c^2 is:

The equation of a straight line passing through the point (2, 3) and inclined at an angle of tan^(-1)(1/2) with the line y+2x=5 , so the equation of the line is/ are: (a) y=3 (b) x=2 3x+4y-18=0 (d) 4x+3y-17=0

Prove that the straight line joining the points A(4, -3, 2) and B(2, -1, -1) is parallel to the straight line joining the point C(7, -3, 5) and D(1, 3, -4).

If the straight line joining the points A(3, 4, -1) and B(4, p, 2) is parallel to the straight line joining the points C(2, 1, q) and D(4, -3, 1), then -

If y= mx +c represents the equation of a straight line parallel to x - axis , then-

If the straight line joining the point (0, 3) and (5, -2) is a tangent to the curve y(x+1)=c , then the value of c will be-

If the stright line x=az+b,y=cz+d and x=a'z+b',y=c'z+d' are coplanar, prove that, (a-a')(d-d')=(b-b')(c-c') .