Question

Show that the set of curves intersect orthogonally:

x² + 4y² = 8 and x² – 2y² = 4.

Answer 1

Given as curve x² + 4y² = 8 ...(1)

and x² – 2y² = 4 ...(2)

Solving the equation (1) & (2)

From the 2nd curve

x² = 4 + y²

Substitute on x² + 4y² = 8

So, the point of intersection of two curves

Differentiate the curves (1) & (2) with respect to x

Now, when m₁ = -1/2 & m₂ = 2

The two curves intersect orthogonally if m₁m₂ = - 1

= (-1/√2) x √2 = -1

Thus, the two curves x² + 4y² = 8 & x² - 2y² = 4 intersect orthogonally.