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The locus of a point P (a, ß) moving under the condition that the line y = ax + ß is a tangent to the hyperbola x2/a2 -y2/b2= 1 ?

The locus of a point P (a, ß) moving under the condition that the line y = ax + ß is a
tangent to the hyperbola
x2/a2 -y2/b2= 1 ?

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Tangent to the hyperbola isx2/a2 -y2/b2= 1
y = mx ±\sqrt{a^{2}m^{2}-b^{2}}
Given that y = αx + β is the tangent of hyperbola
⇒ m = α and a2m2 –b2 = β2
∴ a2α2– b2 = β2
Locus is a2x2 – y2= b2 which is hyperbola.
Thanks and Regards
Shaik Aasif
askIITians faculty

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