HSC Science Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Find the equation of the ellipse in the cases given below:

Length of latus rectum 8, eccentricity = `3/5` centre (0, 0) and major axis on x-axis

Find the equation of the ellipse in the cases given below:

Length of latus rectum 4, distance between foci `4sqrt(2)`, centre (0, 0) and major axis as y-axis

Find the equation of the hyperbola in the cases given below:

Foci (± 2, 0), Eccentricity = `3/2`

Find the equation of the hyperbola in the cases given below:

Centre (2, 1), one of the foci (8, 1) and corresponding directrix x = 4

Find the equation of the hyperbola in the cases given below:

Passing through (5, – 2) and length of the transverse axis along x-axis and of length 8 units

Find the vertex, focus, equation of directrix and length of the latus rectum of the following:

y² = 16x

Find the vertex, focus, equation of directrix and length of the latus rectum of the following:

x² = 24y

Find the vertex, focus, equation of directrix and length of the latus rectum of the following:

y² = – 8x

Find the vertex, focus, equation of directrix and length of the latus rectum of the following:

x² – 2x + 8y + 17 = 0

Find the vertex, focus, equation of directrix and length of the latus rectum of the following:

y² – 4y – 8x + 12 = 0

Identify the type of conic and find centre, foci, vertices, and directrices of the following:

`x^2/25 + y^2/9` = 1

Identify the type of conic and find centre, foci, vertices, and directrices of the following:

`x^2/3 + y^2/10` = 1

Identify the type of conic and find centre, foci, vertices, and directrices of the following:

`x^2/25 - y^2/144` = 1

Identify the type of conic and find centre, foci, vertices, and directrices of the following:

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

Prove that the length of the latus rectum of the hyperbola `x^2/"a"^2 - y^2/"b"^2` = 1 is `(2"b"^2)/"a"`

Show that the absolute value of difference of the focal distances of any point P on the hyperbola is the length of its transverse axis

Identify the type of conic and find centre, foci, vertices, and directrices of the following:

`(x - 3)^2/225 + (y - 4)^2/289` = 1

Identify the type of conic and find centre, foci, vertices, and directrices of the following:

`(x + 1)^2/100 + (y - 2)^2/64` = 1

Identify the type of conic and find centre, foci, vertices, and directrices of the following:

`(x + 3)^2/225 + (y - 4)^2/64` = 1

Identify the type of conic and find centre, foci, vertices, and directrices of the following:

`(y - 2)^3/25 + (x + 1)^2/16` = 1