The curves y + ax^2 +b and y = 2x^2 +cx have a common tangent at the point (-1,0).
Find a, b and c.
Firstly, (-1,0) is a common point thus.Originally Posted by jayson81
Substitute that into the second function,
Thus, the second function has equation,
Since we say that these two function have a common tangent means the equation of the tangent through point (-1,0) is the same. Remember from analytic geomtery that two lines having same slope at same point are the same. Same thing here the tangent lines share a point thus they need to have the same slope.
The slope at for the first function is,
at is .
The slope for the second is,
All we need is to find "b" in,
since (-1,0) is on the curve we have,
Which is not true.
Thus, either you erred in the formulation of your question or there is no such numbers.
I got the same result as ThePerfectHacker, but I find that the solution works . . .
Since is on both curves, we have:The curves and have a common tangent at the point .
Find , and .
Since the slopes are equal at , we have:
Since , we get: . . . and hence:
The parabolas are: . and
They share the common point where they both have slope