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The locus of a point P( , ) moving under the condition that the line y= x+ is a tangent to the hyperbola x^2 a^2 - y^2 b^2 =1 is

Options

  1. Aan ellipse
  2. Ba circle
  3. Ca parabola
  4. Da hyperbola

Correct answer

D. a hyperbola

Step-by-step solution

Tangent to the hyperbola x^2 a^2 - y^2 b^2 =1 is y=m x a^2 m^2-b^2 Given that y= x+ is the tangent of hyperbola m= and a^2 m^2-b^2= ^2 a ^2 ^2- b ^2= ^2 Locus is a^2 x^2-y^2=b^2 which is hyperbola.

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