MHB Finding the Length of TN on a Tangent of the Curve y = x^2

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To find the length of TN on the tangent to the curve y = x^2 at point P(3,9), the slope of the tangent is calculated as dy/dx = 6. The equation of the tangent line is y = 6x - 9, which intersects the x-axis at point T(3/2, 0). Since PN is perpendicular to the x-axis, point N must have the same x-coordinate as point P, which is 3, making N(3, 0). The length of TN can then be determined using the distance formula between points T and N.
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The tangent P(3,9) on the curve y = x^2, cuts the x-axis at T and PN is perpendicular to the x-axis. Find the length of TN.

So far I have:

dy/dx = 2x
dy/dx = 6

y - 9 = 6(x - 3)
y = 6x - 9

Making point T (3/2, 0), but how do you find point N?

Thank you.
 
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