Question

The equation of parabola is y² = ax + ay. Find its vertex, focus, directrix, axis and length of latus rectum

Answer 1

y² – ay = ax

y² – ay+\(\frac{a^2}{4}\)= ax +\(\frac{a^2}{4}\)

y –\(\frac{a^2}2\)= ax+\(\frac{a}4\)

Y² = 4AX

Where: Y = y –\(\frac{a}2,\)X=x+\(\frac{a}4,\)

4A = a ie. A = a/4

Vertex \(-\frac{a}2,\frac{a}2\)

Focus \(0,\frac{a}2\)

Directrix \(x+\frac{a}2=0\)

Axis \(y-\frac{a}2=0\)

Length of latus rectum = a