Thread: GR11 Math: finding endpoints of chord within a circle.

Given...

1. Point P is on the line and is 10 units from the origin. Determine the coordinates of P.

I've gotten this far...

So:

.

Then .

Plugging in y...





This is where I'm stuck since I cannot factor it. When the quadratic formula is applied, the number inside the brackets is a negative number.

2. Given...

From a lighthouse, the range of visibility on a clear day is 40km. On a coordinate system, where O(0,0) represents the lighthouse, a ship is travelling on a course represented by . Between which two points on the course can the ship be seen from the lighthouse?

I got this far...




Plugging it in...





Again, I am stuck with the same problem. I get a negative number when the quadratic formula is applied.

What am I doing wrong here? Thank you so much!

N.

Originally Posted by nathan02079

Given...

1. Point P is on the line and is 10 units from the origin. Determine the coordinates of P.

I've gotten this far...

So:

Are these signs supposed to be different?

Hello, nathan02079!

In your "distance formula", you're square-rooting when you should square.

2. From a lighthouse, the range of visibility on a clear day is 40 km.
On a coordinate system, where O(0,0) represents the lighthouse,
a ship is travelling on a course represented by: .
Between which two points on the course can the ship be seen from the lighthouse?

Code:

                        |
                        |     *
                        | *
                  Q   * |
                  o     |
              *    *    |
      P   *         *   |
      o              *  |
  *         *         * |
                  *    *|
  - - - - - - - - - - - * - - - -
                        |O

and have coordinates such that: .

We want: .

So we have: .

Factor: .

Then: .


The ship can be seen from to

Originally Posted by pickslides

Are these signs supposed to be different?

Whoops, typo there. :/

Originally Posted by Soroban

Hello, nathan02079!

In your "distance formula", you're square-rooting when you should square.

Code:

                        |
                        |     *
                        | *
                  Q   * |
                  o     |
              *    *    |
      P   *         *   |
      o              *  |
  *         *         * |
                  *    *|
  - - - - - - - - - - - * - - - -
                        |O

and have coordinates such that: .

We want: .

So we have: .

Factor: .

Then: .


The ship can be seen from to

Wow, duh! Thanks for stating the obvious! Darn, I never pay attention.

Thank you!

N.

SOLUTION #1:




Points of intersection: (9.6, -2.8), (6,8)

SOLUTION #2:




Points of intersection: (-24, 32), (-40,0)

Thanks again!