Chapter 9.1, Problem 6E

To determine

To find: The two lines with which the tangent line to a parabola at a point $P$ makes equal angles.

Answer to Problem 6E

The tangent line to a parabola at a point $P$ makes equal angles with the line through $P$ parallel to the axis of symmetry and the line through $P$ and focus.

Explanation of Solution

Calculation:

The first line is through the point $P$ parallel to the axis of symmetry of the parabola and the second line is joining the points $P$ and focus of the parabola.

These both line makes equal angles with the tangent line to a parabola at a point $P$ .

Therefore, the tangent line to a parabola at a point $P$ makes equal angles with the line through $P$ parallel to the axis of symmetry and the line through $P$ and focus.