Let C be the circle of radius unity centred at the origin. If two positive numbers `x_1 and x_2` are such that the line passing through `(x_1,-1) and (x_2, 1)` is tangent to C then `x_1*x_2`

Derive the equation of the line passing through two points ( x_ 1,y_1) and ( x_2,y_2)

A circle passes through (2,1) and x+2y=1 is a tangent to it at (3,-1). Find its equation.

Equation of the circle , centred at the origin , whose radius equals the distance between the lines x = -1 and x = 1 , is

If the radius of the circle passing through the origin and touching the line x+y=2 at (1, 1) is r units, then the value of 3sqrt2r is

A curve C passes through origin and has the property that at each point (x,y) on it the normal line at that point passes through (1,0) The equation of a common tangent to the curve C and the parabola y^(2)=4x is

A curve C passes through origin and has the property that at each point (x, y) on it the normal line at that point passes through (1, 0) . The equation of a common tangent to the curve C and the parabola y^2 = 4x is

A curve C passes through origin and has the property that at each point (x, y) on it the normal line at that point passes through (1, 0) . The equation of a common tangent to the curve C and the parabola y^2 = 4x is

The centre of a circle is (2x-1, 3x++1) and radius is 10 units. Find the value of x if the circle passes through the point (-3, -1) .

The centre of a circle is (2x-1, 3x++1) and radius is 10 units. Find the value of x if the circle passes through the point (-3, -1) .

A circle with its centre on the line y=x+1 is drawn to pass through the origin and touch the line y=x+2 .The centre of the circle is