THE CIRCLE X2+Y2-4X-8Y+16=0 rolls up the tangent to it at (2+âˆš3 , 3) by 2 units , assuming the x axis as horizontal , find the equation of the circle in the new position- ...

prove that the polars of any point with respect to a system of coaxal circles all pass through a fixed point and that the two points are equidistant from the radical axis and subtend a right angle at a limiting point of the s ...

The chord of contact of the pair of tangents drawn from each point on the line 2x+y=4 to the circle {{x}^{2}}+{{y}^{2}}=1 pass through the point a) (1/2, â€“ 1/4) b) (1/2, 1/4) c) (â€“ 1/2, 1/4) d) (â€“ 1/2, â€“ 1/4) ...

The equation of the circle passing through the points (0, 0),(0,b) and (a,b) is a) {{x}^{2}}+{{y}^{2}}+ax+by=0 b) {{x}^{2}}+{{y}^{2}}-ax+by=0 c) {{x}^{2}}+{{y}^{2}}+x+3y=0 d) {{x}^{2}}+{{y}^{2}}+ax-by=0 ...

If the radical axis of circles {{x}^{2}}+{{y}^{2}}-6x-8y+p=0 and {{x}^{2}}+{{y}^{2}}-8x-6y+14=0 passes through the point (1, â€“ 1), then p is equal to ...