Thread: unit hyperbola and circle

Please see attachment. That there is a unit circle. The hyperbola is also unit. This is all the information you need. Yes, I threw in an ellipse too.


I.

Find the y coordinate of the point where the two red lines intersect.
Find the y axis intercept of the purple line.

II.

If the two blue lines are railroad tracks receding into the distance and meeting at the totally flat horizon line (light green), and an ant observer is standing on the x axis, what is the real distance from the ant of the two y values found in part I?

Originally Posted by rainer

Please see attachment. That there is a unit circle. The hyperbola is also unit. This is all the information you need. Yes, I threw in an ellipse too.


I.

Find the y coordinate of the point where the two red lines intersect.
Find the y axis intercept of the purple line.

II.

If the two blue lines are railroad tracks receding into the distance and meeting at the totally flat horizon line (light green), and an ant observer is standing on the x axis, what is the real distance from the ant of the two y values found in part I?

I like geometry, and would like to do this. That being said, the red and purple lines are indistinguishable. At least for me.

Originally Posted by Drexel28

I like geometry, and would like to do this. That being said, the red and purple lines are indistinguishable. At least for me.

See attachment.

The purple line is now yellow. Hope it's clearer. I also added a second, smaller ellipse. An additional challenge is to find the semi-minor and semi-major axes of the smaller ellipse.


Edit: I just realized the semi-minor axis of the smaller ellipse can't be found without further information. So nevermind about that part. The other challenges still stand.