MathematicsChapter 7: Conic Section
Parabola With Vertical Axis
For x^2=4ay, focus=(0,a) and directrix y=-a; signs determine opening.
Learning objectives
- State the rule for parabola with vertical axis.
- Solve a parabola with vertical axis problem step by step.
- Check the result, restrictions, notation, and units.
Definition
For x^2=4ay, focus=(0,a) and directrix y=-a; signs determine opening.
Mathematical form
focus=(0
y=-a
Where / symbols
- Parabola with vertical axis
- For x^2=4ay, focus=(0,a) and directrix y=-a; signs determine opening.
CONCEPT AND RULE
For x^2=4ay, focus=(0,a) and directrix y=-a; signs determine opening.
METHOD
For parabola with vertical axis, 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
x^2=-12y opens downward with focus (0,-3).
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 with vertical axis
- 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:
- x^2=-12y opens downward with focus (0,-3).
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 with vertical axis
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Parabola With Vertical Axis
Sticky Notes · Formula and Worked Revision
Core Idea
- For x^2=4ay, focus=(0,a) and directrix y=-a; signs determine opening.
Rule / Formula
- For x^2=4ay, focus=(0,a) and directrix y=-a; signs determine opening.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- x^2=-12y opens downward with focus (0,-3).
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- For x^2=4ay, focus=(0,a) and directrix y=-a; signs determine opening.
- Worked pattern: x^2=-12y opens downward with focus (0,-3).
- Final check: domain, sign, notation, units, and reasonableness.
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