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Translated Hyperbolas
(x-h)^2a2-(y-k)^2b2=1 has centre (h,k) and translated asymptotes.
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Translated Hyperbolas
What is it?
(x-h)^2a2-(y-k)^2b2=1 has centre (h,k) and translated asymptotes.
In simple words
- (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.
Important terms
Translated hyperbolas: (x-h)^2a2-(y-k)^2b2=1 has centre (h,k) and translated asymptotes.
What you should learn
- State the rule for translated hyperbolas.
- Solve a translated hyperbolas problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
(x-h)^2a2-(y-k)^2b2=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
How it works
- 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.
Remember
- Translated hyperbolas
- rule
- worked example
- worked example
How the ideas connect
Worked example: (x-1)frac24-(y+2)frac29=1 has centre (1,-2).
Deeper understanding
Go beyond memorising Translated Hyperbolas. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: (x-1)frac24-(y+2)frac29=1 has centre (1,-2).
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Translated hyperbolas
- rule
- worked example
- Translated hyperbolas: (x-h)^2a2-(y-k)^2b2=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 d
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Translated Hyperbolas: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Translated hyperbolas
- rule
- worked example
- Translated hyperbolas: (x-h)^2a2-(y-k)^2b2=1 has centre (h,k) and translated asymptotes.
Important formulas
- Translated hyperbolas
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Translated hyperbolas
rule
worked example
Translated hyperbolas: (x-h)^2a2-(y-k)^2b2=1 has centre (h,k) and translated asymptotes.
(x-h)^2a2-(y-k)^2b2=1 has centre (h,k) and translated asymptotes.
- Definition
- (x-h)^2a2-(y-k)^2b2=1 has centre (h,k) and translated asymptotes.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Translated Hyperbolas.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Translated Hyperbolas and say why it fits.
Mistake
Q4. State one common mistake students make about Translated Hyperbolas.
Exam note
Q5. Write a short exam note on Translated Hyperbolas: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.