Commerce (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

Fill in the blank to make the following a true statement:

U' ∩ A = _____

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola.

`x^2/16 - y^2/9 = 1`

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola.

`y^2/9 - x^2/27 = 1`

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola.

9y² – 4x² = 36

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola.

16x² – 9y² = 576

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola.

5y² – 9x² = 36

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola.

49y² – 16x² = 784

Find the centre, eccentricity, foci and directrice of the hyperbola .

16x² − 9y² + 32x + 36y − 164 = 0

Find the centre, eccentricity, foci and directrice of the hyperbola.

 x² − y² + 4x = 0

Find the centre, eccentricity, foci and directrice of the hyperbola .

x² − 3y² − 2x = 8.

Find the eccentricity of the hyperbola, the length of whose conjugate axis is \[\frac{3}{4}\] of the length of transverse axis.

If the distance between the foci of a hyperbola is 16 and its ecentricity is \[\sqrt{2}\],then obtain its equation.

Write the coordinates of the foci of the hyperbola 9x² − 16y² = 144.

Write the equation of the hyperbola of eccentricity \[\sqrt{2}\],  if it is known that the distance between its foci is 16.

If the foci of the ellipse \[\frac{x^2}{16} + \frac{y^2}{b^2} = 1\] and the hyperbola \[\frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25}\] coincide, write the value of b².

If e₁ and e₂ are respectively the eccentricities of the ellipse \[\frac{x^2}{18} + \frac{y^2}{4} = 1\]

and the hyperbola \[\frac{x^2}{9} - \frac{y^2}{4} = 1\] then write the value of 2 e₁² + e₂².

If e₁ and e₂ are respectively the eccentricities of the ellipse \[\frac{x^2}{18} + \frac{y^2}{4} = 1\] and the hyperbola \[\frac{x^2}{9} - \frac{y^2}{4} = 1\] , then the relation between e₁ and e₂ is

The equation of the conic with focus at (1, −1) directrix along x − y + 1 = 0 and eccentricity \[\sqrt{2}\] is