Find the slope of a common tangent to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` and a concentric circle of radius `rdot`

If any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 intercepts equal lengths l on the axes, then find ldot

If the line y=mx+c is a tangent to the ellipse x^(2)+2y^(2)=4 , find c

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

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

The slopes of the common tanents of the ellipse (x^2)/4+(y^2)/1=1 and the circle x^2+y^2=3 are (a) +-1 (b) +-sqrt(2) (c) +-sqrt(3) (d) none of these

The values of 'm' for which a line with slope m is common tangent to the hyperbola x^2/a^2-y^2/b^2=1 and parabola y^2 = 4ax can lie in interval:

Statement 1 : Tangents are drawn to the ellipse (x^2)/4+(y^2)/2=1 at the points where it is intersected by the line 2x+3y=1 . The point of intersection of these tangents is (8, 6). Statement 2 : The equation of the chord of contact to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 from an external point is given by (x x_1)/(a^2)+(y y_1)/(b^2)-1=0

If y=2x+c is tangent to the circle x^(2)+y^(2)=16 find c.

Prove that the chords of constant of perpendicular tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touch another fixed ellipse (x^(2))/(a^(4))+(y^(2))/(b^(4))=(1)/((a^(2)+b^(2)))