Question

# The curves and intersect orthogonally, then

Hint:

### We are given two curves. They intersect orthogonally. We have to find the relation between the variables.

## The correct answer is:

### The curves are as follows:

ax^{2} + by^{2} = 1 ...(1)

Ax^{2} + By^{2} = 1 ...(2)

We will take the derivative of equation (1) w.r.t x.

2ax + 2by=0

2by= -2ax

This is this slope of first curve. We will call it slope1.

In the same way we will take the derivative of equation (2) w.r.t x

2Ax + 2By = 1

We will call it slope2.

The two curves are orthogonal. So, the product of their slope is -1.

Slope1 × Slope2 = -1

We will substitute (3) in (1)

We will substitute (4) in (2)

Divide (5) by (6)

This is the required answer.

.

For such questions, we should be careful while taking the derivative.

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