Question

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On WH 06 , we looked at the intersection point of two distinct normal lines to the parabola, then computed the coordinates of the limit of that intersection point as one normal line approached the oth

Answer 1

The intersection point of two distinct normal lines to a parabola is known as the vertex of the parabola. The coordinates of the vertex can be found by setting the equations of the two normal lines equal to each other and solving for the coordinates.

Step-by-step explanation:

A normal line to a parabola is a line that is perpendicular to the tangent to the parabola at a given point. The intersection point of two distinct normal lines to a parabola is known as the vertex of the parabola. The coordinates of the vertex can be found by setting the equations of the two normal lines equal to each other and solving for the coordinates.

For example, if the equations of the two normal lines are y = mx + b1 and y = nx + b2, we can set them equal to each other:

mx + b1 = nx + b2

Simplifying, we get:

(m-n)x = b2 - b1

We can solve for x by dividing both sides by (m-n):

x = (b2 - b1)/(m-n)

Once we have the value of x, we can substitute it back into one of the equations to find the value of y.