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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Select the correct option from the given alternatives: The length of latus rectum of the parabola x2 – 4x – 8y + 12 = 0 is _________ - Mathematics and Statistics

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प्रश्न

Select the correct option from the given alternatives:

The length of latus rectum of the parabola x2 – 4x – 8y + 12 = 0 is _________

पर्याय

  • 4

  • 6

  • 8

  • 10

MCQ

उत्तर

8

Explanation:

Hint: The given equation can be written as:

x2 – 4x + 4 = 8y – 12 + 4

∴ (x – 2)2 = 8(y – 1)

This is of the form X2 = 4bY, where 4b = 8

∴ l(L.R.) = 4b = 8

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Conic Sections - Parabola
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Conic Sections - Miscellaneous Exercise 7 [पृष्ठ १७६]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board
पाठ 7 Conic Sections
Miscellaneous Exercise 7 | Q I. (2) | पृष्ठ १७६

संबंधित प्रश्‍न

Find co-ordinate of focus, equation of directrix, length of latus rectum and the co-ordinate of end points of latus rectum of the parabola:

y2 = –20x


Find co-ordinate of focus, equation of directrix, length of latus rectum and the co-ordinate of end points of latus rectum of the parabola:

x2 = –8y


Find the equation of the parabola with vertex at the origin, axis along X-axis and passing through the point (3, 4)


Find the equation of the parabola with vertex at the origin, axis along X-axis and passing through the point (1, –6)


For the parabola 3y2 = 16x, find the parameter of the point (3, – 4).


Find coordinates of the point on the parabola. Also, find focal distance.

2y2 = 7x whose parameter is –2


Find coordinate of focus, vertex and equation of directrix and the axis of the parabola y = x2 – 2x + 3


Find the equation of tangent to the parabola y2 = 36x from the point (2, 9)


Select the correct option from the given alternatives:

The coordinates of a point on the parabola y2 = 8x whose focal distance is 4 are _______


Select the correct option from the given alternatives:

The area of the triangle formed by the line joining the vertex of the parabola x2 = 12y to the endpoints of its latus rectum is _________


Select the correct option from the given alternatives:

The equation of the parabola having (2, 4) and (2, –4) as endpoints of its latus rectum is _________


Select the correct option from the given alternatives:

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


Answer the following:

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


Answer the following:

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


Answer the following:

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


Answer the following:

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


Answer the following:

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


Answer the following:

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.


Answer the following:

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


The equation of the directrix of the parabola 3x2 = 16y is ________.


Let P: y2 = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of `π/4` with the line y = 3x + 5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is ______.


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Let y = mx + c, m > 0 be the focal chord of y2 = –64x, which is tangent to (x + 10)2 + y2 = 4. Then, the value of `4sqrt(2)` (m + c) is equal to ______.


If the normal at the point (1, 2) on the parabola y2 = 4x meets the parabola again at the point (t2, 2t), then t is equal to ______.


Which of the following are not parametric coordinates of any point on the parabola y2 = 4ax?


The equation to the line touching both the parabolas y2 = 4x and x2 = –32y is ______.


The equation of the parabola whose vertex and focus are on the positive side of the x-axis at distances a and b respectively from the origin is ______.


Through the vertex O of parabola y2 = 4x, chords OP and OQ are drawn at right angles to one another, where P and Q are points on the parabola. If the locus of middle point of PQ is y2 = 2(x – l), then value of l is ______.


A circle of radius 2 unit passes through the vertex and the focus of the parabola y2 = 2x and touches the parabola y = `(x - 1/4)^2 + α`, where α > 0. Then (4α – 8)2 is equal to ______.


If vertex of a parabola is (2, –1) and the equation of its directrix is 4x – 3y = 21, then the length of its latus rectum is ______.


The cartesian co-ordinates of the point on the parabola y2 = –16x, whose parameter is `1/2`, are ______.


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