MathematicsChapter 6: Analytical Geometry
Circle in Standard Form
(x-h)^2+(y-k)^2=r^2 has centre (h,k) and radius r.
Learning objectives
- State the rule for circle in standard form.
- Solve a circle in standard form problem step by step.
- Check the result, restrictions, notation, and units.
Definition
(x-h)2+(y-k)2=r2 has centre (h,k) and radius r.
Where / symbols
- Circle in standard form
- (x-h)^2+(y-k)^2=r^2 has centre (h,k) and radius r.
CONCEPT AND RULE
(x-h)2+(y-k)2=r2 has centre (h,k) and radius r.
METHOD
For circle 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
x2+y2-4x+6y-12=0 becomes (x-2)2+(y+3)2=25.
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 circle 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:
- x2+y2-4x+6y-12=0 becomes (x-2)2+(y+3)2=25.
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
- Circle 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.Circle in Standard Form
Sticky Notes · Formula and Worked Revision
Core Idea
- (x-h)2+(y-k)2=r2 has centre (h,k) and radius r.
Rule / Formula
- (x-h)2+(y-k)2=r2 has centre (h,k) and radius r.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- x2+y2-4x+6y-12=0 becomes (x-2)2+(y+3)2=25.
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)2+(y-k)2=r2 has centre (h,k) and radius r.
- Worked pattern: x^2+y^2-4x+6y-12=0 becomes (x-2)^2+(y+3)^2=25.
- Final check: domain, sign, notation, units, and reasonableness.
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