I need to find the tangent line to an ellipse by only knowing the slope of a parallel line to the tangent line

Question

bharat bajaj · Answer

Equation of ellipse : x²/a² + y²/b² = 1

Let the point of tangency, whose coordinates will also satisfy the equation of the tangent line, be (p,q).

The slope of the tangent line is equal to the value of the derivative at the point of tangency.

Derivating wrt to x,

2x/a² + 2yy'/b² = 0

y' = -(b²/a²)(x/y)

Therefore, evaluating y' when x = p and y = q,

m = -(b²/a²)(p/q)

Solving for, say, q, we have

q = -(b²/a²)(p/m)

Since (p, q) lies on the ellipse, it satisfies the ellipse's equation; thus,

p²/a² + q²/b² = 1

Substitute for q from the earlier result:

p²/a² + [-(b²/a²)(p/m)]²/b² = 1

This simplifies to

(p²/a²)[1 + (b²/(m²a²))] = 1
Thanks

Bharat Bajaj
IIT delhi

askiitians faculty

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

I need to find the tangent line to an ellipse by only knowing the slope of a parallel line to the tangent line

I need to find the tangent line to an ellipse by only knowing the slope of a parallel line to the tangent line

1 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Algebra

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship