how do we find the equation of a parabola if the vertex is at origin and directrix is at x=3
Share
how do we find the equation of a parabola if the vertex is at origin and directrix is at x=3
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
y^2+12x=0
Step-by-step explanation:
As we have vertex at the origin i.e. (0,0) and directrix is x=3, a line parallel to y-axis,
it must have a focus at (-3,0).
Equation of the parabola represents locus of a point (x,y), which moves so that its distance from x=3 and (-3,0) are equal. Hence, equation of parabola is
(x-(-3))^2+(y-0)^2=(x-3)^2
or (x+3)^2+y^2=(x-3)^2
or x^2+6x+9+y^2=x^2-6x+9
or y^2+12x=0
graph{y^2+12x=0 [-27.59, 12.41, -10.08, 9.92]}