Question

please explain in brief how to find common tangent of two conic sections

Answer 1

any example??

Answer 2

well, like common tangent of circle x^2+y^2=a^2 and the parabola y^2=4bx

Answer 3

Two tangents at most.

Answer 4

I am not sure ... but it think it's worth trying.

Answer 5

i wanna know the method to find the equations

Answer 6

they both will have same slope.
slope of tangent of m = -x/y
while slope of parabola will be = 2b/y

Answer 7

@satellite73

Answer 8

slope of parabola?

Answer 9

@ishaan94, help me please

Answer 10

Hmm so a circle and a parabola.
Let the equation of circle be \(y^2 + x^2 = a^2\) and parabola's be \(y^2 = 4bx\).
Slope be m. Equation of tangent to parabola is, \(y=mx + \frac{b}{m}\).

Perpendicular distance from point of contact of the tangent to circle's center is radius. \[\frac{b}{\sqrt{m^2 + m^4}}=a \implies \frac{b^2}{m^4+m^2} = a^2\]
You will need to solve this equation now.