Question:

Find the value of the constant for which the line is a tangent to the curve

Attempt:

, ,

I can't continue because Im getting a negative value inside the square root, where did I go wrong?

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- Apr 26th 2008, 08:35 AMlooi76[SOLVED] Find the value of constant k in tangent
**Question:**

Find the value of the constant for which the line is a tangent to the curve

**Attempt:**

, ,

I can't continue because Im getting a negative value inside the square root, where did I go wrong? - Apr 26th 2008, 08:40 AMMoo
Hello,

They're not saying that y+2x=k is the equation of the curve, but that it is tangent to the curve.

This means that at a given point, the tangent to the curve will have y+2x=k as an equation.

The tangent to the curve at a point of absciss a is :

Hence, calculate the derivative of and then... think :D - Apr 26th 2008, 08:52 AMlooi76
Thanks Moo!

, ,

I still can't continue! - Apr 26th 2008, 08:56 AMMathstud28
- Apr 26th 2008, 09:03 AMlooi76
- Apr 26th 2008, 09:06 AMMathstud28
- Apr 26th 2008, 09:07 AMlooi76
- Apr 26th 2008, 09:09 AMMathstud28
- Apr 26th 2008, 09:10 AMMathstud28
- Apr 26th 2008, 09:15 AMMoo
Ok, so let's do it step by step :

Let

Hence the equation of the tangent line at a point is :

So the only point where there will be a tangent line whose equation is in the form will be for

Hence

:) - Apr 29th 2008, 08:52 PMThePerfectHacker
In the case of a parabola a line is tangent if and only if it has one intersection point with the parabola.

Thus, is tangent to if and only if has exactly one solution. That means, the quadradic has exactly one solution. That happens precisely when the discriminant vanishes, thus, . - Nov 25th 2012, 11:23 PMHiteshRulZZZRe: [SOLVED] Find the value of constant k in tangent

Here is how you do it.. Easy and Simple

Line:**y = k-2x**

Curve:**y = x²-6x+14**

__Workings__

**k-2x = x²-6x+14**

x²-6x+2x+14-k = 0

x²-4x+14-k = 0

a=1, b=-4, c=(14-k)

[I]Use this Equation[/I] ----**b²-4ac**

**b²-4ac**<---- Here's your Answer!!!

Replace..

=(-4)²-[4(14-k)]

=16-(56-4k)

=16-56+4k

4k = -16+56

4k = 40

k = 40/4

k = 10