Chapter 9.1, Problem 91E

To determine

To find: The coordinates of the point of tangency to the parabola $y^2-8x=0$ and equation of tangent line $x-y+2=0$ with the help of graphing of graphing utility.

Answer to Problem 91E

The coordinates of the points of tangency to the parabola $y^2-8x=0$ with equation of tangent line $x-y+2=0$ are $\left(2,4\right)$ .

Explanation of Solution

Given information:

The equation of parabola is $y^2-8x=0$ and the equation of the tangent line is $x-y+2=0$ .

Calculation:

The graph of the function of the parabola $y^2-8x=0$ with the line $x-y+2=0$ is shown below:

  

Figure(1)

As shown in the graph that the line $x-y+2=0$ meets the parabola $y^2-8x=0$ at only one point $\left(2,4\right)$ .

Therefore, the coordinates of the point of tangency to the parabola $y^2-8x=0$ with tangent line $x-y+2=0$ are $\left(2,4\right)$ .