HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the equation of the hyperbola referred to its principal axes:

which passes through the points (6, 9) and (3, 0)

Find the equation of the hyperbola referred to its principal axes:

whose vertices are (± 7, 0) and end points of conjugate axis are (0, ±3)

Find the equation of the hyperbola referred to its principal axes:

whose foci are at (±2, 0) and eccentricity `3/2`

Find the equation of the hyperbola referred to its principal axes:

whose length of transverse and conjugate axis are 6 and 9 respectively

Find the equation of the hyperbola referred to its principal axes:

whose length of transverse axis is 8 and distance between foci is 10

Find the equation of the tangent to the hyperbola:

3x² – y² = 4 at the point `(2, 2sqrt(2))`

Find the equation of the tangent to the hyperbola:

3x² – 4y² = 12 at the point (4, 3)

Find the equation of the tangent to the hyperbola:

`x^2/144 - y^2/25` = 1 at the point whose eccentric angle is `pi/3`

Find the equation of the tangent to the hyperbola:

`x^2/16 - y^2/9` = 1 at the point in a first quadratures whose ordinate is 3

Find the equation of the tangent to the hyperbola:

9x² – 16y² = 144 at the point L of latus rectum in the first quadrant

Show that the line 3x – 4y + 10 = 0 is tangent till the hyperbola x² – 4y² = 20. Also find the point of contact

If the 3x – 4y = k touches the hyperbola `x^2/5 - (4y^2)/5` = 1 then find the value of k

Find the equations of the tangents to the hyperbola `x^2/25 - y^2/9` = 1 making equal intercepts on the co-ordinate axes

Find the equations of the tangents to the hyperbola 5x² – 4y² = 20 which are parallel to the line 3x + 2y + 12 = 0

Select the correct option from the given alternatives

The eccentricity of rectangular hyperbola is

Select the correct option from the given alternatives:

Eccentricity of the hyperbola 16x² − 3y² − 32x − 12y − 44 = 0 is

Select the correct option from the given alternatives:

If the line 2x − y = 4 touches the hyperbola 4x² − 3y² = 24, the point of contact is

Select the correct option from the given alternatives:

The foci of hyperbola 4x² − 9y² − 36 = 0 are

Answer the following:

For the hyperbola `x^2/100−y^2/25` = 1, prove that SA. S'A = 25, where S and S' are the foci and A is the vertex

Answer the following:

Find the equation of the hyperbola in the standard form if Length of conjugate axis is 5 and distance between foci is 13.