#1**+4 **

I graphed it here

https://www.desmos.com/calculator/ercszykueb

I let m=tan(t) where t is the angle that is made with the positive x axis (for any line with a gradient of m)

It is the locus of points that make the intersection of the solid red and green lines that is relevant.

t is in radians

You can slide the value of t to see what happens to this intersection.

The locus is definitely a hyperbola (just by visual inspection)

Since it is a hyperbola the eccentricity has to be more than 1 so I am going for 3

Of course you were meant to nut it out without graphing. You could probably do this just by thinking about a few points.

My way is more fun and much more time consuming.

Melody Sep 30, 2019