MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 11

                        

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

6 years ago

Answers : (1)

bharat bajaj
IIT Delhi
askIITians Faculty
122 Points
							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
6 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 101 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details