







A common tangent to two general parabolas 
20151115 

From Kind: Hi,
I want to find the common tangent of two general parabolas, but i don't know if it's possible or not.
If it's possible, please make a tutorial.
The first parabola equation : Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
The second parabola equation : Gx^2 + Hxy + Iy^2 + Jx + Ky + L = 0.
I need this because i want to find the equation of Beloch fold. (Huzita  Hatori 6th axiom)
However if you know any other method to find Beloch folds equation, I am open for any suggestions. Answered by Chris Fisher. 





A common tangent to two curves 
20090302 

From Jay: For what values of a and b will the parabola y = x^2 + ax + b be tangent to the curve y = x^3 at (1,1)? Answered by Penny Nom. 





Two tangent circles and common tangents 
20081201 

From Alan: Radius of big circle 30cm, radius of small circle 10 cm. From the diagram, the radius from the tangent do not form a semicircle but at an angle. Find the perimeter of the band around both the circle. May need to use trigonometry to find reflex angle AOB, CMD and get the major arc length AB and minor arc length CD Answered by Penny. 





Two tangent circles 
20080822 

From Michele: A circle of radius 2 is externally tangent to a circle of radius 8,
How do you find the length of their common tangent. Answered by Penny Nom. 





A common tangent line 
20070220 

From chris: I have this problem I have been working on for days and cannot figure it out. it states: Find the two points on the curve y=x^4  2x^2  x that have a common tangent line.
I know you use the first derivative to find the tangent line so if it is a common tangent line should you find two of the exact same tangent line equations at two coordinate points? Answered by Chris Fisher. 





A common tangent line 
20041005 

From Shanup: The xaxis is a common tangent of y = x^2 and y = x^3. Find the equation of another common tangent. Answered by Penny Nom. 





Common tangents 
20010408 

From Anne: I have been working on this problem for a while but I'm not sure I'm getting the right answer: Find the common tangents of 2y=x^{2} and 2y=x^{2}16 Thanks for the help. :) Answered by Harley Weston`. 

