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 ?

Question

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 ?

SHAIK AASIF AHAMED · Answer

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

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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 ?

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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 ?

1 Answers

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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 ?