169k views
0 votes
How can the equation of a parabola be derived when given the focus and the directrix?

User Lakeesha
by
8.9k points

1 Answer

7 votes
The distance between any point (x0,y0) on the parabola and the focus (m,n) is the same as the distance between (x0,y0) and the directrix line ax+by+c. The distance between (x0,y0) and focus (a,b) is \sqrt((x-m)^2+(y-n)^2). The distance between (x0,y0) and ax+by+c is |ax0+by0+c|/\sqrt(m^2+n^2).  Equalize these two expressions.
User Chadee Fouad
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories