MathematicsChapter 7: Conic Section
Tangent To A Hyperbola
At (x1,y1), tangent is xx1/a^2-yy1/b^2=1 for the horizontal standard form.
Learning objectives
- State the rule for tangent to a hyperbola.
- Solve a tangent to a hyperbola problem step by step.
- Check the result, restrictions, notation, and units.
Definition
At (x1,y1), tangent is xx1/a^2-yy1/b^2=1 for the horizontal standard form.
Formula
x=3.
Where / symbols
- Tangent to a hyperbola
- At (x1,y1), tangent is xx1/a^2-yy1/b^2=1 for the horizontal standard form.
CONCEPT AND RULE
At (x1,y1), tangent is xx1/a^2-yy1/b^2=1 for the horizontal standard form.
METHOD
For tangent to a hyperbola, 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
At (3,0) on xfrac29-yfrac24=1, tangent x=3.
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 tangent to a hyperbola
- 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:
- At (3,0) on xfrac29-yfrac24=1, tangent x=3.
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
- Tangent to a hyperbola
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Tangent To A Hyperbola
Sticky Notes · Formula and Worked Revision
Core Idea
- At (x1,y1), tangent is xx1/a^2-yy1/b^2=1 for the horizontal standard form.
Rule / Formula
- At (x1,y1), tangent is xx1/a^2-yy1/b^2=1 for the horizontal standard form.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- At (3,0) on xfrac29-yfrac24=1, tangent x=3.
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
- At (x1,y1), tangent is xx1/a^2-yy1/b^2=1 for the horizontal standard form.
- Worked pattern: At (3,0) on xfrac29-yfrac24=1, tangent x=3.
- Final check: domain, sign, notation, units, and reasonableness.
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