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Question: If tangent and normal to a rectangular hyperbola xy = c<sup>2</sup> cut off intercepts a<sub>1</sub>...

If tangent and normal to a rectangular hyperbola xy = c2 cut off intercepts a1 and a2 on one axis and b1, b2 on the other, then:

A

a1 = b1

B

a2 = b2

C

a1a2=b1b2\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}

D

a1a2 + b1b2 = 0

Answer

a1a2 + b1b2 = 0

Explanation

Solution

Tangents and normals are at 900. Product of slopes is -1.

(b1a1)(b2a2)=1\left( - \frac{b_{1}}{a_{1}} \right)\left( - \frac{b_{2}}{a_{2}} \right) = - 1

a1a2 + b1b2 = 0