13) Find points on the curve  \frac{x^2}{9} + \frac{y^2}{16} = 1 at which the tangents are  (b) parallel to y-axis 

Answers (1)

Parallel to y-axis means the slope of the tangent is  \infty , means the slope of normal is 0
We know that slope of the tangent at a given point on the given curve is given by  \frac{dy}{dx}
Given the equation of the curve is 
\frac{x^2 }{9} + \frac{y^2 }{16} = 1 \Rightarrow 9y^2 = 144(1-16x^2)
18y\frac{dy}{dx} = 144(1-32x)
\frac{dy}{dx} = \frac{-32x}{18y} = \infty
Slope of normal = -\frac{dx}{dy} = \frac{18y}{32x} = 0
From this we can say that y = 0
Now. when y = 0,  \frac{x^2 }{9} + \frac{0^2 }{16} \Rightarrow 1 = x = \pm 3
Hence, the coordinates are (3,0) and (-3,0)

Most Viewed Questions

Related Chapters

Preparation Products

Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Buy Now
Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
Buy Now
NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
Buy Now
NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
NEET Foundation + Knockout NEET 2025 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions