MathematicsChapter 7: Conic Section
Hyperbola in Standard Form
x^2/a^2-y^2/b^2=1 has c^2=a^2+b^2 and foci (+-c,0).
Learning objectives
- State the rule for hyperbola in standard form.
- Solve a hyperbola in standard form problem step by step.
- Check the result, restrictions, notation, and units.
Definition
xfrac2a2-yfrac2b2=1 has c2=a2+b2 and foci (+-c,0).
Formula
c=5.
Where / symbols
- Hyperbola in standard form
- x^2/a^2-y^2/b^2=1 has c^2=a^2+b^2 and foci (+-c,0).
CONCEPT AND RULE
xfrac2a2-yfrac2b2=1 has c2=a2+b2 and foci (+-c,0).
METHOD
For hyperbola 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 xfrac29-yfrac216=1, c=5.
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 hyperbola 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 xfrac29-yfrac216=1, c=5.
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
- Hyperbola 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.Hyperbola in Standard Form
Sticky Notes · Formula and Worked Revision
Core Idea
- xfrac2a2-yfrac2b2=1 has c2=a2+b2 and foci (+-c,0).
Rule / Formula
- xfrac2a2-yfrac2b2=1 has c2=a2+b2 and foci (+-c,0).
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- For xfrac29-yfrac216=1, c=5.
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
- xfrac2a2-yfrac2b2=1 has c2=a2+b2 and foci (+-c,0).
- Worked pattern: For xfrac29-yfrac216=1, c=5.
- Final check: domain, sign, notation, units, and reasonableness.
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