MathematicsChapter 7: Conic Section
Translated Ellipses
Replace x,y by x-h,y-k to move the centre to (h,k).
Learning objectives
- State the rule for translated ellipses.
- Solve a translated ellipses problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Replace x,y by x-h,y-k to move the centre to (h,k).
Where / symbols
- Translated ellipses
- Replace x,y by x-h,y-k to move the centre to (h,k).
CONCEPT AND RULE
Replace x,y by x-h,y-k to move the centre to (h,k).
METHOD
For translated ellipses, 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)frac216+(y+1)frac24=1 has centre (2,-1).
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 ellipses
- 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)frac216+(y+1)frac24=1 has centre (2,-1).
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 ellipses
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Translated Ellipses
Sticky Notes · Formula and Worked Revision
Core Idea
- Replace x,y by x-h,y-k to move the centre to (h,k).
Rule / Formula
- Replace x,y by x-h,y-k to move the centre to (h,k).
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- (x-2)frac216+(y+1)frac24=1 has centre (2,-1).
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
- Replace x,y by x-h,y-k to move the centre to (h,k).
- Worked pattern: (x-2)frac216+(y+1)frac24=1 has centre (2,-1).
- Final check: domain, sign, notation, units, and reasonableness.
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