# Tangent line to the curve

Hobold

## Homework Statement

This is a very basic problem, though it did confuse me a little:

Find the tangent equations to the curve $$x=3t^2+1 \ , \ y = 2t^3+2$$ which intercepts the point (4,3).

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## The Attempt at a Solution

I took $$\frac{dy}{dx} = t = \frac{y-y_0}{x-x_0} = \frac{y-3}{x-4} \rightarrow y=t(x-4)+3$$

What to do next? I don't think the equation works for all t.

Mentor

## Homework Statement

This is a very basic problem, though it did confuse me a little:

Find the tangent equations to the curve $$x=3t^2+1 \ , \ y = 2t^3+2$$ which intercepts the point (4,3).
Are you sure the above is right? If x = 4, then t = +/-1, but when t = 1, y = 4 and when t = -1, y = 0.

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## The Attempt at a Solution

I took $$\frac{dy}{dx} = t = \frac{y-y_0}{x-x_0} = \frac{y-3}{x-4} \rightarrow y=t(x-4)+3$$

What to do next? I don't think the equation works for all t.

Hobold
Yes, I'm sure, those are the functions.

I believe the problem asks for a tangent of the graphic which will intercept the point (4,3) in R^2, which is not necessarily in the graphic of the function.

Mentor
OK, I misunderstood.

So let's say we're talking about the point on the curve whose coordinates are (x0, y0), that correspond to t = t0.

Can you use the parametric equations to write x0 and y0 in terms of t0. Then use the point (4, 3) and calculate the slope of the line segment between (x0, y0) and (4, 3), which you know is equal to t0.