Show that the point a' is the reflection of the point a in the line `zbarb+barzb+c=0,` If `a'barb+barab+c=0.`

Show that the point P(a, b + c), Q(b, c +a) and R(c, a + b) are collinear.

Find the distance of the line 4x+7y+5=0 from the point (1,2) along the line 2x-y=0 .

Let C be the set of curves having the property that the point of intersection of tangent with y-axis is equidistant from the point of tangency and origin (0,0) If C_(3) in C C_(3): is passing through (2,4). If (x)/(a)+(y)/(b)=1. is tangent to C_(3) , then

Let C be the set of curves having the property that the point of intersection of tangent with y-axis is equidistant from the point of tangency and origin (0,0) If C_(1),C_(2) in C C_(1) : Curve is passing through (1,0) C_(2) : Curve is passing through (-1,0) The number of common tangents for C_(1) and C_(2) is

Assuming that straight lines work as the plane mirror for a point, find the image of the point (1,2) in the line x - 3y + 4 =0 .

Let C be the set of curves having the property that the point of intersection of tangent with y-axis is equidistant from the point of tangency and origin (0,0) If common tangents of C_(1) and C_(2) form an equilateral triangle, where C_(1),C_(2) in C and C_(1) : Curve passes through f(2,0), then C_(2) may passes through

Show that the points A (4, 2), B (7, 5) and C (9, 7) are three points lying on a same line.

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0,- 4) and B (8,0).

Show that inverse of a point a with respect to the circle |z-c|=R(aandc are complex numbers, centre and redius R) is the point c+(R^(2))/(bara-barc),