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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Select the correct option from the given alternatives: If the focus of the parabola is (0, –3) its directrix is y = 3 then its equation is - Mathematics and Statistics

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प्रश्न

Select the correct option from the given alternatives:

If the focus of the parabola is (0, –3) its directrix is y = 3 then its equation is

पर्याय

  • x2 = – 12y

  • x2 = 12y

  • y2 = 12x

  • y2 = −12x

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उत्तर

x2 = – 12y

Explanation;


SP2 = PM2

∴ (x – 0)2 + (y + 3)2 = `|(y - 3)/sqrt(1)|^2`

∴ x2 + y2 + 6y + 9 = y2 – 6y + 9

∴ x2 = – 12y

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

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 7 Conic Sections
Miscellaneous Exercise 7 | Q I. (3) | 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:

5y2 = 24x


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3x2 = 8y


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:

3y2 = –16x


Find the equation of the parabola with vertex at the origin, axis along Y-axis and passing through the point (–10, –5).


Find the equation of the parabola whose vertex is O(0, 0) and focus at (–7, 0).


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).


For the parabola 3y2 = 16x, find the parameter of the point (27, –12).


Find the focal distance of a point on the parabola y2 = 16x whose ordinate is 2 times the abscissa


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2y2 = 7x whose parameter is –2


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Show that the circle touches the directrix of the parabola.


Select the correct option from the given alternatives:

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


Answer the following:

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

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Answer the following:

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


Answer the following:

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


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:

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

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


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