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Tangent to an Ellipse
At (x1,y1) on xfrac2a2+yfrac2b2=1, tangent is xx1/a2+yy1/b2=1.
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Tangent to an Ellipse
What is it?
At (x1,y1) on xfrac2a2+yfrac2b2=1, tangent is xx1/a2+yy1/b2=1.
In simple words
- At (x1,y1) on xfrac2a2+yfrac2b2=1, tangent is xx1/a2+yy1/b2=1.
- Worked pattern: At (3,4) on xfrac225+yfrac216=1 is 3x/25+y/4=1.
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Tangent to an ellipse: At (x1,y1) on x^2a2+y^2b2=1, tangent is xx1/a2+yy1/b2=1.
What you should learn
- State the rule for tangent to an ellipse.
- Solve a tangent to an ellipse problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
At (x1,y1) on xfrac2a2+yfrac2b2=1, tangent is xx1/a2+yy1/b2=1.
CONCEPT AND RULE
At (x1,y1) on xfrac2a2+yfrac2b2=1, tangent is xx1/a2+yy1/b2=1.
METHOD
For tangent to an ellipse, 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 (3,4) on xfrac225+yfrac216=1 is 3x/25+y/4=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 tangent to an ellipse
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
- Tangent to an ellipse
- rule
- worked example
- worked example
How the ideas connect
Worked example: At (3,4) on xfrac225+yfrac216=1 is 3x/25+y/4=1.
Deeper understanding
Go beyond memorising Tangent to an Ellipse. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: At (3,4) on xfrac225+yfrac216=1 is 3x/25+y/4=1.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Tangent to an ellipse
- rule
- worked example
- Tangent to an ellipse: At (x1,y1) on x^2a2+y^2b2=1, tangent is xx1/a2+yy1/b2=1.
- CONCEPT AND RULE: At (x1,y1) on x^2a2+y^2b2=1, tangent is xx1/a2+yy1/b2=1.
- METHOD: For tangent to an ellipse, identify the given information and required result. Select the matching d
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 Tangent to an Ellipse: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Tangent to an ellipse
- rule
- worked example
- Tangent to an ellipse: At (x1,y1) on x^2a2+y^2b2=1, tangent is xx1/a2+yy1/b2=1.
Important formulas
- Tangent to an ellipse
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Tangent to an ellipse
rule
worked example
Tangent to an ellipse: At (x1,y1) on x^2a2+y^2b2=1, tangent is xx1/a2+yy1/b2=1.
At (x1,y1) on xfrac2a2+yfrac2b2=1, tangent is xx1/a2+yy1/b2=1.
- Definition
- At (x1,y1) on xfrac2a2+yfrac2b2=1, tangent is xx1/a2+yy1/b2=1.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Tangent to an Ellipse.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Tangent to an Ellipse and say why it fits.
Mistake
Q4. State one common mistake students make about Tangent to an Ellipse.
Exam note
Q5. Write a short exam note on Tangent to an Ellipse: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.