Thread: Tangent to a curve; constant k

Hi guys,

I am confused with this one. Would I still use dy/dx? If not, could someone please provide me with a formula?

Find the value of the constant k for which the line y + 2x = k is a tangent to the curve y = x ² - 6x + 14

Thanks

Originally Posted by laoch

Hi guys,

I am confused with this one. Would I still use dy/dx? If not, could someone please provide me with a formula?

Find the value of the constant k for which the line y + 2x = k is a tangent to the curve y = x ² - 6x + 14

Thanks

The simplest approach is to solve for the intersection points of the line and parabola and then force the value of k to be such that there's only one intersection point:

.... (1)

.... (2)

Start solving equations (1) and (2) simultaneously:

.

There will be only one solution (and hence will be a tangent to ) if the discriminant of this quadratic is equal to zero:

Thank you so much