MathematicsChapter 7: Conic Section
Translated Hyperbolas
(x-h)^2/a^2-(y-k)^2/b^2=1 has centre (h,k) and translated asymptotes.
Learning objectives
- State the rule for translated hyperbolas.
- Solve a translated hyperbolas problem step by step.
- Check the result, restrictions, notation, and units.
Definition
(x-h)^2a2-(y-k)^2b2=1 has centre (h,k) and translated asymptotes.
Where / symbols
- Translated hyperbolas
- (x-h)^2/a^2-(y-k)^2/b^2=1 has centre (h,k) and translated asymptotes.
CONCEPT AND RULE
(x-h)^2a2-(y-k)^2b2=1 has centre (h,k) and translated asymptotes.
METHOD
For translated hyperbolas, 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-1)frac24-(y+2)frac29=1 has centre (1,-2).
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 translated hyperbolas
- 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-1)frac24-(y+2)frac29=1 has centre (1,-2).
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
- Translated hyperbolas
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Translated Hyperbolas
Sticky Notes · Formula and Worked Revision
Core Idea
- (x-h)^2a2-(y-k)^2b2=1 has centre (h,k) and translated asymptotes.
Rule / Formula
- (x-h)^2a2-(y-k)^2b2=1 has centre (h,k) and translated asymptotes.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- (x-1)frac24-(y+2)frac29=1 has centre (1,-2).
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
- (x-h)^2a2-(y-k)^2b2=1 has centre (h,k) and translated asymptotes.
- Worked pattern: (x-1)frac24-(y+2)frac29=1 has centre (1,-2).
- Final check: domain, sign, notation, units, and reasonableness.
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