Grade 12Analytical Geometry
tangent
how to find the equation of common tangent to circle,parabola,ellipse,hyperbola
1 Answer
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.
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