The curve represents a parabola with vertex at the origin.

MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

The curve

y^{2}=4ax

represents a parabola with vertex at the origin. (i) State the standard equation of a parabola whose axis is the

x

-axis and whose vertex is the origin. Also mention its vertex and axis. (ii) If a point

P(x_{1},y_{1})

lies on this parabola, derive an expression for the parameter

a

in terms of

x_{1}

and

y_{1}

. (iii) Explain why a point with

x_{1}<0

cannot satisfy the equation

y^{2}=4ax

for any real

a