JEE Main & Advanced Mathematics Conic Sections Question Bank

done Numerical Value Type Questions - Hyperbola Total Questions - 15

• question_answer1)
  Consider the set of hyperbola \[xy=k,\,\,\,k\in R.\] Let \[{{e}_{1}}\] be the eccentricity when \[k=4\] and \[{{e}_{2}}\] be the eccentricity when \[k=9\] then \[{{e}_{1}}-{{e}_{2}}=\]
  View Solution play_arrow

• question_answer2)
  If the foci of the ellipse \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and the hyperbola \[\frac{{{x}^{2}}}{144}-\frac{{{y}^{2}}}{81}=\frac{1}{25}\] coincide, then find the value \[{{b}^{2}}.\]
  View Solution play_arrow

• question_answer3)
  Find the eccentricity of the conjugate hyperbola of the hyperbola \[{{x}^{2}}-3{{y}^{2}}=1.\]
  View Solution play_arrow

• question_answer4)
  A tangent drawn to hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] at \[P\left( \frac{\pi }{6} \right)\] forms a triangle of area \[3{{a}^{2}}\] square units, with coordinate axes, then the square of its eccentricity.
  View Solution play_arrow

• question_answer5)
  Find the eccentricity of the hyperbola \[\frac{\sqrt{1999}}{3}\left( {{x}^{2}}-{{y}^{2}} \right)=1.\]
  View Solution play_arrow

• question_answer6)
  Find the eccentricity of the hyperbola whose latus rectum 12 and semi-conjugate axis is\[2\sqrt{3}\].
  View Solution play_arrow

• question_answer7)
  If the eccentricity and length of latus rectum of a hyperbola are \[\frac{\sqrt{13}}{3}\]and \[\frac{10}{3}\]units respectively, then find the length of the transverse axis.
  View Solution play_arrow

• question_answer8)
  If P is any point on the hyperbola \[\frac{{{\left( x-1 \right)}^{2}}}{9}-\frac{{{\left( y+1 \right)}^{2}}}{16}=1\] and \[{{S}_{1}}\] and \[{{S}_{2}}\] are its foci then find value of \[\left| {{S}_{1}}P-{{S}_{2}}P \right|.\]
  View Solution play_arrow

• question_answer9)
  The straight line \[x+y=\sqrt{2}p\] touches the hyperbola \[4{{x}^{2}}-\text{ }9{{y}^{2}}=36,\] then find value of \[{{p}^{2}}.\]
  View Solution play_arrow

• question_answer10)
  If e and e' are the eccentricities of the ellipse \[5{{x}^{2}}+9{{y}^{2}}=45\] and the hyperbola \[5{{x}^{2}}-4{{y}^{2}}=45\] respectively, then find value of \[ee'.\]
  View Solution play_arrow

• question_answer11)
  If the latus rectum of a hyperbola subtends \[60{}^\circ \]angle at the other focus, then find its eccentricity.
  View Solution play_arrow

• question_answer12)
  If distance between directrices of a rectangular hyperbola is 10, then find distance between its foci.
  View Solution play_arrow

• question_answer13)
  Find the length of the latus rectum of the hyperbola \[xy-3x-3y+7=0.\]
  View Solution play_arrow

• question_answer14)
  Let LL' be the latus rectum through the focus of the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and A' be the farther vertex If \[\Delta \,\,A'LL'\] is equilateral and the eccentricity of the hyperbola (axes are coordinate axes) is \[\left( 1+\frac{1}{k} \right)\] then find k.
  View Solution play_arrow

• question_answer15)
  Find the eccentricity of the hyperbola \[9{{x}^{2}}-16{{y}^{2}}+72x-32y-16=0.\]
  View Solution play_arrow