MathematicsChapter 7: Conic Section
Tangent To A Parabola
For y^2=4ax, tangent at parameter t is ty=x+at^2.
Learning objectives
- State the rule for tangent to a parabola.
- Solve a tangent to a parabola problem step by step.
- Check the result, restrictions, notation, and units.
Definition
For y2=4ax, tangent at parameter t is ty=x+at2.
Formula
ty=x+at2. Worked example
Where / symbols
- Tangent to a parabola
- For y^2=4ax, tangent at parameter t is ty=x+at^2.
CONCEPT AND RULE
For y2=4ax, tangent at parameter t is ty=x+at2.
METHOD
For tangent to a parabola, 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
For y2=4x at t=2, 2y=x+4.
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 parabola
- 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:
- For y2=4x at t=2, 2y=x+4.
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 parabola
- 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 Parabola
Sticky Notes · Formula and Worked Revision
Core Idea
- For y2=4ax, tangent at parameter t is ty=x+at2.
Rule / Formula
- For y2=4ax, tangent at parameter t is ty=x+at2.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- For y2=4x at t=2, 2y=x+4.
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
- For y2=4ax, tangent at parameter t is ty=x+at2.
- Worked pattern: For y2=4x at t=2, 2y=x+4.
- Final check: domain, sign, notation, units, and reasonableness.
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