Question

Find the equation of the hyperbola whose directrix is 2x+y=1

Answer 1

Answer:

1 answer · Mathematics

Answer

Hyperbola is the locus of a point which is at a distance from a line(the directrix) which is equal to e times the distance from a fixed point(the focus).

So let (x,y) be any arbitrary point lying on the hyperbola.

Its distance from the directrix will be equal to (x+2y-1)/(1^2+2^2) say n

And its distance from the focus will be equal to [(x-2)^2+(y-1)^2]^(1/2) say m

Equate n=em

Then on solving the equation you will get the equation of the hyperbola.

Step-by-step explanation: