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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Select the correct option from the given alternatives: The coordinates of a point on the parabola y2 = 8x whose focal distance is 4 are _______ - Mathematics and Statistics

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प्रश्न

Select the correct option from the given alternatives:

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

पर्याय

  • `(1/2, ±2)`

  • `(1, ±2sqrt(2))`

  • (2, ± 4)

  • none of these

MCQ
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उत्तर

The coordinates of a point on the parabola y2 = 8x whose focal distance is 4 are (2, ± 4)

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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. (4) | 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


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:

3x2 = 8y


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)


Find the equation of the parabola with vertex at the origin, axis along X-axis and passing through the point (2, 3)


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


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

y2 = 12x whose parameter is `1/3`


For the parabola y2 = 4x, find the coordinate of the point whose focal distance is 17


Find the equation of tangent to the parabola y2 = 12x from the point (2, 5)


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


The tower of a bridge, hung in the form of a parabola have their tops 30 meters above the roadway and are 200 meters apart. If the cable is 5 meters above the roadway at the centre of the bridge, find the length of the vertical supporting cable 30 meters from the centre.


Select the correct option from the given alternatives:

The line y = mx + 1 is a tangent to the parabola y2 = 4x, if m is _______


Select the correct option from the given alternatives:

The endpoints of latus rectum of the parabola y2 = 24x 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 _________


Answer the following:

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

2y2 = 17x


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:

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

16x2 + 25y2 = 400


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 ________.


The locus of the mid-point of the line segment joining the focus of the parabola y2 = 4ax to a moving point of the parabola, is another parabola whose directrix is ______.


Let the tangent to the parabola S: y2 = 2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then, the area (in sq.units) of the triangle PQR is equal to ______.


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 ______.


The centre of the circle passing through the point (0, 1) and touching the parabola y = x2 at the point (2, 4) is ______.


If the vertex = (2, 0) and the extremities of the latus rectum are (3, 2) and (3, –2) then the equation of the parabola 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 ______.


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