A point on the downward parabola has focal distance 15 and distance 7 from the x-axis. Find p.

01 / Standard#Your turn

x^2=-py,\quad p>0

Official paper · jm01-2025 · I.11 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

The point’s ordinate must be −7.

Hint 2

Its distance to the directrix equals its focal distance.

Worked solution

Identify the directrix using the standard coefficient 4a.
$y_{\rm directrix}=\frac p4,\quad y_A=-7$
Apply the focus-directrix definition.
$7+\frac p4=15\implies p=32$

E: 32.

Checks and common pitfalls: The coefficient p here is four times the focal distance parameter.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Identify the directrix using the standard coefficient 4a.
$y_{\rm directrix}=\frac p4,\quad y_A=-7$
Apply the focus-directrix definition.
$7+\frac p4=15\implies p=32$

Think first. Reveal a hint when the class is ready.

2025 JM01