HSC Science (Computer Science) 11th Standard - Maharashtra State Board Question Bank Solutions

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A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y−interecpt is

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The angle between the line `sqrt(3)x - y - 2` = 0 and `x - sqrt(3)y + 1` = 0 is 

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If kx + 2y − 1 = 0 and 6x − 4y + 2 = 0 are identical lines, then determine k

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Find the value of k if the slope of the line passing through the points P(3, 4), Q(5, k) is 9

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Find the value of k the points A(1, 3), B(4, 1), C(3, k) are collinear

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Find the value of k the point P(1, k) lies on the line passing through the points A(2, 2) and B(3, 3)

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Find the equation of the line containing the point T(7, 3) and having inclination 90°.

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Line through A(h, 3) and B(4, 1) intersect the line 7x − 9y − 19 = 0 at right angle Find the value of h

Answer the following:

Find the

1. lengths of the principal axes
2. co-ordinates of the foci
3. equations of directrices
4. length of the latus rectum
5. distance between foci
6. distance between directrices of the ellipse:

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

Find the

1. lengths of the principal axes.
2. co-ordinates of the focii
3. equations of directrics
4. length of the latus rectum
5. distance between focii
6. distance between directrices of the ellipse:

3x² + 4y² = 12

Find the

1. lengths of the principal axes.
2. co-ordinates of the focii 
3. equations of directrics 
4. length of the latus rectum
5. distance between focii 
6. distance between directrices of the ellipse:

2x² + 6y² = 6

Find the 

1. lengths of the principal axes. 
2. co-ordinates of the focii 
3. equations of directrices 
4. length of the latus rectum
5. distance between focii 
6. distance between directrices of the ellipse:

3x² + 4y² = 1

Find the equation of the ellipse in standard form if eccentricity = `3/8` and distance between its foci = 6

Find the equation of the ellipse in standard form if the distance between directrix is 18 and eccentricity is `1/3`.

Find the equation of the ellipse in standard form if the minor axis is 16 and eccentricity is `1/3`.

Find the equation of the ellipse in standard form if the distance between foci is 6 and the distance between directrix is `50/3`.

Find the equation of the ellipse in standard form if the latus rectum has length of 6 and foci are (±2, 0).

Find the equation of the ellipse in standard form if passing through the points (−3, 1) and (2, −2)

Find the equation of the ellipse in standard form if the dist. between its directrix is 10 and which passes through `(-sqrt(5), 2)`.

Find the equation of the ellipse in standard form if eccentricity is `2/3` and passes through `(2, −5/3)`.