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.

Results 1 to 3 of 3

- June 13th 2006, 05:57 PM #1jayson81Guest

- June 13th 2006, 07:03 PM #2

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

Originally Posted by**jayson81**

Substitute that into the second function,

Thus,

solve,

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,

at is

Thus, thus,

All we need is to find "b" in,

since (-1,0) is on the curve we have,

thus,

Thus,

Which is not true.

Thus, either you erred in the formulation of your question or there is no such numbers.

- June 14th 2006, 06:08 AM #3

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 11,921
- Thanks
- 784

Hello, jayson81!

I got the same result as ThePerfectHacker, but I find that the solution works . . .

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:

Therefore: .

The parabolas are: . and

They share the common point where they both have slope