For the parabola having focus and directrix

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

For the parabola having focus (a,0)(a,0) and directrix x=−ax=-a, a point P(x,y)P(x,y) belongs to the curve only if (a) (x−a)2+y2=(y+a)2(x-a)^{2}+y^{2}=(y+a)^{2} (b) y2=4a(x−a)y^{2}=4a(x-a) (c) (x−a)2+y2=(x+a)2(x-a)^{2}+y^{2}=(x+a)^{2} (d) (x+a)2+y2=(x−a)2(x+a)^{2}+y^{2}=(x-a)^{2}

Related theory

Browse the problem library