Q. 2 C5.0( 1 Vote )

# Show that the following set of curves intersect orthogonally :x2 + 4y2 = 8 and x2 – 2y2 = 4.

Given:

Curves x2 + 4y2 = 8 ...(1)

& x2 – 2y2 = 4 ...(2)

Solving (1) & (2),we get,

from 2nd curve,

x2 = 4 + 2y2

Substituting on x2 + 4y2 = 8,

4 + 2y2 + 4y2 = 8

6y2 = 4

y2

y = ±

Substituting on y = ±, we get,

x2 = 4 + 2(±)2

x2 = 4 + 2()

x2 = 4 +

x2

x = ±

x = ±

The point of intersection of two curves (,) & (,)

Now ,Differentiating curves (1) & (2) w.r.t x, we get

x2 + 4y2 = 8

2x + 8y. = 0

8y. = – 2x

...(3)

x2 – 2y2 = 4

2x – 4y.0

x – 2y.0

4yx

...(4)

At (,) in equation(3),we get

m1

At (,) in equation(4),we get

m2 = 1

when m1 & m2

× = – 1

Two curves x2 + 4y2 = 8 & x2 – 2y2 = 4 intersect orthogonally.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Tangents & Normals (Concept Builder Class)FREE Class
Test your knowledge of Tangents & Normals (Quiz)FREE Class
Human Evolution | An Important ConceptFREE Class
Interactive Quiz | Biotechnology - 03FREE Class
Human Evolution38 mins
Rapid Quiz challenge - Cell Structure & Cell Division52 mins
Different high order thinking questions based on DNA structure39 mins