Finding the X-coordinate of a normal to the tangent

[Count Duckula]

Homework Statement

Tangent to C at point P(2,7) has an equation of y=3x+1.

Point Q also lies on C and is perpendicular to the tangent,
show that the X-coordinate is [1/3(2+√6)]

Homework Equations

curve C has equation y= x³-2x²-x+9
dy/dx = 3x²-4x-1

The Attempt at a Solution

gradient of normal has to = -1/3, right? considering that the tangent that is is perpendicular to is +3
I'm not sure as, the point that the normal is passing through hasn't been specified.

Here is the actual question: http://i259.photobucket.com/albums/hh299/the-real-guitar-hero/CapturePNGnnn_zpsd170ce09.png

Part C.

 

[Mark44]

Homework Statement

Tangent to C at point P(2,7) has an equation of y=3x+1.

Point Q also lies on C and is perpendicular to the tangent,
show that the X-coordinate is [1/3(2+√6)]

Homework Equations

curve C has equation y= x³-2x²-x+9
dy/dx = 3x²-4x-1

The Attempt at a Solution

gradient of normal has to = -1/3



I'm not sure as the point, that the normal is passing through hasn't been specified.

Here is the actual question: http://i259.photobucket.com/albums/hh299/the-real-guitar-hero/CapturePNGnnn_zpsd170ce09.png

Part C.

Problems involving derivatives should be posted in the Calculus & Beyond section. I am moving this thread to that section.