MathematicsChapter 7: Conic Section

Parabola in Standard Form

For y^2=4ax, focus=(a,0), directrix x=-a, and latus rectum length=4a.

Learning objectives

State the rule for parabola in standard form.
Solve a parabola in standard form problem step by step.
Check the result, restrictions, notation, and units.

Definition

For y^2=4ax, focus=(a,0), directrix x=-a, and latus rectum length=4a.

Mathematical form

focus=(a

x=-a

length=4a. Worked example

a=2 and focus

Where / symbols

Parabola in standard form: For y^2=4ax, focus=(a,0), directrix x=-a, and latus rectum length=4a.

CONCEPT AND RULE

For y^2=4ax, focus=(a,0), directrix x=-a, and latus rectum length=4a.

METHOD

For parabola in standard form, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.

WORKED EXAMPLE

For y²=8x, a=2 and focus=(2,0).

COMMON MISTAKE

Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.

How to solve parabola in standard form

Identify the mathematical objects, givens, restrictions, and required result.
Choose and write the relevant definition, theorem, or formula.
Substitute with brackets and carry out one justified step per line.
Simplify, state the final answer clearly, and verify it in the original setting.

Worked example

Worked example:
For y²=8x, a=2 and focus=(2,0).

In simple words

Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.

Key points

Parabola in standard form
rule
worked example

Exam preparation

Exam Focus

Quick revision

Revision Zone

Review the key facts, formulas and checks before you move on.