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

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

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!

2. 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 $(6,35)$.

3. What's in English words?

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

5. 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.