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What is the product of length of perpendicular drawn from any point on the hyperbola to its asymtotes. ..given only a and b...

What is the product of length of perpendicular drawn from any point on the hyperbola to its asymtotes. ..given only a and b...

Grade:12

1 Answers

Vijay Mukati
askIITians Faculty 2590 Points
6 years ago
Dear Student,

For the hyperbola x2/a2 – y2/b2 = 1 ,

Te two asymptotes are given by x/a + y/b = 0 or x/a- y/b=0. We can rewrite these as bx + ay = 0 and bx – ay = 0 respectively.

Now the length of perpendicular for any point P(x,y) on to these asymptotees are given by (bx+ay)/(sqrt(a2+b2)) and (bx-ay)/(sqrt(a2+b2)) respectively.

And thus the product of these lengths can be simplied easily to (b2x2 – a2y2)/(a2+b2)

Thanks.

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