The curves and intersect orthogonally, then

The correct answer is:

The curves are as follows:
ax² + by² = 1            ...(1)
Ax² + By² = 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.
 
 
 
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For such questions, we should be careful while taking the derivative.