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# how to find the equation of common tangent to circle,parabola,ellipse,hyperbola

24 Points
11 years ago

Hi,

1] you take a straight line say: Ax+By=1

2] eliminate x(or y) using this line equation and the equation of curve 1

3]then you will have an equation purely in y's it will be quadratic

4]now since this straight line is the tangent to the curve 1 apply the condition of existence of a unique root that is b^2-4ac=0 you will get a relation between the coefficients A and B

5]similarly follow the same procedure with the curve 2 and again equate b^2-4ac to 0 and again u will get a relation btw A & B

6]solve both the relations and get the values of A & B and hence the common tangent.