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

• Oct 16th 2009, 10:21 AM
s3a
TWO tangent lines to curve y = x^2, x-coordinates of points of tangency = ?
Question:
There are two tangent lines to the curve http://gauss.vaniercollege.qc.ca/web...394a860011.png 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!
• Oct 16th 2009, 11:14 AM
Scott H
A tangent line passing through $\displaystyle (6,35)$ may not have a slope of value $\displaystyle 2\cdot 6=12$ there, as the slope of such a line is constant even when $\displaystyle x$ varies. What we're really looking for are values of $\displaystyle x_0$ such that

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

passes through $\displaystyle (6,35)$.
• Oct 16th 2009, 02:23 PM
s3a
• Oct 16th 2009, 03:13 PM
hjortur
In his formula $\displaystyle x_0$ is the x-coordinate of the point of tangency.
The point where the tangent line touches the graph.
• Oct 17th 2009, 06:11 PM
aidan
Quote:

Originally Posted by s3a
Question:
There are two tangent lines to the curve http://gauss.vaniercollege.qc.ca/web...394a860011.png which pass through the point (6,35). Find the x-coordinates of the points of tangency.!

Quote:

There are two tangent lines ...
Quote:

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 $\displaystyle y=x^2$ AND passes thorough (6,35) [for this line x<6].

& the x coordinate of the line that is tangent to the curve $\displaystyle y=x^2$ 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:
$\displaystyle y_1 = 2x_1 + b$ (that passes thorough (6,35) AND is tangent to $\displaystyle y=x^2$

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

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