Find the equation of the common tangent of `y^2=4a x` and `x^2=4a ydot`

Find the equation of the common tangent to the curves y^2=8x and xy=-1.

The equation of the common tangent to the parabolas y^2= 4ax and x^2= 4by is given by

Find the equation of the common tangent in the first quadrant of the circle x^2+y^2=16 and the ellipse x^2/25+y^2/4=1 .Also find the length of the intercept of the tangent between the coordinates axes.

Find the equation of the common tangent in the first quadrant of the circle x^2+y^2=16 and the ellipse x^2/25+y^2/4=1 .Also find the length of the intercept of the tangent between the coordinates axes.

The equation of the common tangent between the curve y^2 =4x and xy=-2 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

Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 touch each other. Find the coordinates of the point of contact and the equation of the common tangent at the point of contact.

Find the equations to the common tangents to the two hyperbolas (x^2)/(a^2)-(y^2)/(b^2)=1 and (y^2)/(a^2)-(x^2)/(b^2)=1

The equations of the common tangents to the parabola y = x^2 and y=-(x-2)^2 is/are :

Two circles, each of radius 5 units, touch each other at (1, 2). If the equation of their common tangents is 4x+3y=10 , find the equations of the circles.