Question

In the xy-plane, a parabola defined by the equation y=(x-8)^2 intersects the line defined by the equation y=36 at two points, P and Q. What is the length of PQ?

A) 8
B) 10
C) 12
D) 14

Answer 1

Answer:

12

Step-by-step explanation:

Alright so we are asked to find the intersection of y=(x-8)^2 and y=36.

So plug second equation into first giving:  36=(x-8)^2.

36=(x-8)^2

Take square root of both sides:

$\pm 6=x-8$

Add 8 on both sides:

$8 \pm 6=x$

x=8+6=14 or x=8-6=2

So we have the two intersections (14,36) and (2,36).

We are asked to compute this length.

The distance formula is:

$\sqrt{(14-2)^2+(36-36)^2}$

$\sqrt{14-2)^2+(0)^2$

$\sqrt{14-2)^2$

$\sqrt{12^2}$

$12$.

I could have just found the distance from 14 and 2 because the y-coordinates were the same. Oh well. 14-2=12.