The sum of the slopes of the lines tangent to both the circles `x^2+y^2=1` and `(x-6)^2+y^2=4` is________

The slope of the line touching both the parabolas y^2=4x and x^2=−32y is

If y=4x+c is a tangent to the circle x^(2)+y^(2)=9 , find c.

Find the locus of a point which moves so that the ratio of the lengths of the tangents to the circles x^2+y^2+4x+3=0 and x^2+y^2-6x+5=0 is 2: 3.

Find the slope of the tangent to the curve y = x^(3) – x at x = 2.

The number of common tangents to the circles x^(2) + y^(2) = 4 and x^(2)+y^(2)-6x-8y=24 is

Find the equations to the common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=0

The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the point (1,3) is.

Find the slope of the tangent to the curve y= (x-1)/(x-2), x ne 2 at x = 10.

Find the number of common tangent to the circles x^2+y^2+2x+8y-23=0 and x^2+y^2-4x-10 y+9=0