HSC Science (Computer Science) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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If the parabola y² = 4ax passes through (3, 2) then the length of its latus rectum is ________

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For the following parabola, find focus, equation of the directrix, length of the latus rectum, and ends of the latus rectum:

2y² = 17x

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For the following parabola, find focus, equation of the directrix, length of the latus rectum, and ends of the latus rectum:

5x² = 24y

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Find the Cartesian coordinates of the point on the parabola y² = 12x whose parameter is 2

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Find the Cartesian coordinates of the point on the parabola y² = 12x whose parameter is −3

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Find the co-ordinates of a point of the parabola y² = 8x having focal distance 10

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Find the equation of the tangent to the parabola y² = 9x at the point (4, −6) on it

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Find the equation of the tangent to the parabola y² = 8x at t = 1 on it

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Find the equations of the tangents to the parabola y² = 9x through the point (4, 10).

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Show that the two tangents drawn to the parabola y² = 24x from the point (−6, 9) are at the right angle

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Find the equation of the tangent to the parabola y² = 8x which is parallel to the line 2x + 2y + 5 = 0. Find its point of contact

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A line touches the circle x² + y² = 2 and the parabola y² = 8x. Show that its equation is y = ± (x + 2).

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The slopes of the tangents drawn from P to the parabola y² = 4ax are m₁ and m₂, show that  m₁ − m₂ = k, where k is a constant.

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The slopes of the tangents drawn from P to the parabola y² = 4ax are m₁ and m₂, show that `("m"_1 /"m"_2)` = k, where k is a constant.

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The tangent at point P on the parabola y² = 4ax meets the y-axis in Q. If S is the focus, show that SP subtends a right angle at Q

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Find the
(i) lengths of the principal axes
(ii) co-ordinates of the foci
(iii) equations of directrices
(iv) length of the latus rectum
(v) Distance between foci
(vi) distance between directrices of the curve

16x² + 25y² = 400

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Find the
(i) lengths of the principal axes
(ii) co-ordinates of the foci
(iii) equations of directrices
(iv) length of the latus rectum
(v) Distance between foci
(vi) distance between directrices of the curve

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

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Find the
(i) lengths of the principal axes
(ii) co-ordinates of the foci
(iii) equations of directrices
(iv) length of the latus rectum
(v) Distance between foci
(vi) distance between directrices of the curve

x² − y² = 16

Write the conjugates of the following complex number:

3 + i

Write the conjugates of the following complex number:

3 – i