TWO tangent lines to curve y = x^2, x-coordinates of points of tangency = ?

**s3a** · October 16th 2009, 10:21 AM

Question:
There are two tangent lines to the curve which pass through the point (6,35). Find the x-coordinates of the points of tangency.

My work is attached.

Any help would be greatly appreciated!
Thanks in advance!

**Scott H** · October 16th 2009, 11:14 AM

A tangent line passing through $(6,35)$ may not have a slope of value $2\cdot 6=12$ there, as the slope of such a line is constant even when $x$ varies. What we're really looking for are values of $x_0$ such that

$y-y_0=2x_0(x-x_0)$

passes through $(6,35)$ .

**s3a** · October 16th 2009, 02:23 PM

What's

in English words?

**hjortur** · October 16th 2009, 03:13 PM

In his formula $x_0$ is the x-coordinate of the point of tangency.
The point where the tangent line touches the graph.

**aidan** · October 17th 2009, 06:11 PM

Originally Posted by s3a

Question:
There are two tangent lines to the curve which pass through the point (6,35). Find the x-coordinates of the points of tangency.!

There are two tangent lines ...

which pass through the point (6,35).
Find the x-coordinates of the points of tangency.!

Your worksheet shows an equation for a line (1 line).

You need to show the x coordinate of the line that is tangent to the curve $y=x^2$ AND passes thorough (6,35) [for this line x<6].

& the x coordinate of the line that is tangent to the curve $y=x^2$ AND passes thorough (6,35) [for this ine x>6].

The two tangent lines will intersect at (6,35).

You will have two lines:
LINE 1:
$y_1 = 2x_1 + b$ (that passes thorough (6,35) AND is tangent to $y=x^2$

LINE 2:
$y_2 = 2x_2 + c$ (that passes thorough (6,35) AND is tangent to $y=x^2$

You are looking for x1 and x2.
See the posts by Scott H (& hjortur) it is almost solved.

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