jee-advanced 2003 Q11

jee-advanced · India · screening Conic sections Eccentricity or Asymptote Computation

11. For hyperbola $x ^ { 2 } / \left( \cos ^ { 2 } a \right) - y ^ { 2 } / \left( \sin ^ { 2 } a \right) = 1$ which of the following remains constant with change in ' a ' :
(a) abscissae of vertices
(b) abscissa of foci

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(c) eccentricity
(d) directrix

The minimum value of $f ( x ) = x ^ { 2 } + 2 b x + 2 c ^ { 2 }$ is more than the maximum value of $g ( x ) = - x ^ { 2 } - 2 c x + b ^ { 2 } , x$ being real, for

11. For hyperbola $x ^ { 2 } / \left( \cos ^ { 2 } a \right) - y ^ { 2 } / \left( \sin ^ { 2 } a \right) = 1$ which of the following remains constant with change in ' a ' :\\
(a) abscissae of vertices\\
(b) abscissa of foci

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(c) eccentricity\\
(d) directrix\\

Paper Questions

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