Translated Ellipses

Translated Ellipses

What is it?

Replace x,y by x-h,y-k to move the centre to (h,k).

In simple words

• 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.

Important terms

Translated ellipses: Replace x,y by x-h,y-k to move the centre to (h,k).

What you should learn

• State the rule for translated ellipses.
• Solve a translated ellipses problem step by step.
• Check the result, restrictions, notation, and units.

Full school-level explanation

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

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 ellipses
• rule
• worked example
• worked example

How the ideas connect

Worked example: (x-2)^frac216+(y+1)^frac24=1 has centre (2,-1).

Deeper understanding

Go beyond memorising Translated Ellipses. Connect the definition to reasons, relationships, exceptions, and exam wording.

How the ideas connect

Worked example: (x-2)^frac216+(y+1)^frac24=1 has centre (2,-1).

Common mistakes

Exam focus

Core Idea

Rule / Formula

Method

Worked Example

Exam focus

Quick revision

• Translated ellipses
• rule
• worked example
• 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 def

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 Ellipses: define clearly → explain the main parts → give one example → state one exam caution.