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 tangent to the curve y=2sqrt2x

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

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

The number of common tangents to the circles x^2+y^2=4 and x^2+y^2-6x-8y-24=0 is

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^2-4x-6y-12=0 and x^2+y^2+6x+18y+26=0

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

From an arbitrary point P on the circle x^2+y^2=9 , tangents are drawn to the circle x^2+y^2=1 , which meet x^2+y^2=9 at A and B . The locus of the point of intersection of tangents at A and B to the circle x^2+y^2=9 is (a) x^2+y^2=((27)/7)^2 (b) x^2-y^2((27)/7)^2 (c) y^2-x^2=((27)/7)^2 (d) none of these

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