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Select the correct option from the given alternatives: The equation of the ellipse having foci (+4, 0) and eccentricity 13 is - Mathematics and Statistics

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प्रश्न

Select the correct option from the given alternatives:

The equation of the ellipse having foci (+4, 0) and eccentricity `1/3` is

पर्याय

  • 9x2 + 16y2 = 144

  • 144x2 + 9y2 = 1296

  • 128x2 + 144y2 = 18432

  • 144x2 + 128y2 = 18432

MCQ

उत्तर

The equation of the ellipse having foci (+4, 0) and eccentricity `1/3` is 128x2 + 144y2 = 18432

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Conic Sections - Ellipse
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Conic Sections - Miscellaneous Exercise 7 [पृष्ठ १७७]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board
पाठ 7 Conic Sections
Miscellaneous Exercise 7 | Q I. (12) | पृष्ठ १७७

संबंधित प्रश्‍न

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:

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 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 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)`.


A tangent having slope `–1/2` to the ellipse 3x2 + 4y2 = 12 intersects the X and Y axes in the points A and B respectively. If O is the origin, find the area of the triangle


Show that the line 8y + x = 17 touches the ellipse x2 + 4y2 = 17. Find the point of contact


Determine whether the line `x + 3ysqrt(2)` = 9 is a tangent to the ellipse `x^2/9 + y^2/4` = 1. If so, find the co-ordinates of the pt of contact


Find k, if the line 3x + 4y + k = 0 touches 9x2 + 16y2 = 144


Find the equation of the tangent to the ellipse 4x2 + 7y2 = 28 from the point (3, –2).


Find the equation of the tangent to the ellipse 2x2 + y2 = 6 from the point (2, 1).


Find the equation of the tangent to the ellipse `x^2/25 + y^2/4` = 1 which are parallel to the line x + y + 1 = 0.


Show that the locus of the point of intersection of tangents at two points on an ellipse, whose eccentric angles differ by a constant, is an ellipse


P and Q are two points on the ellipse `x^2/"a"^2 + y^2/"b"^2` = 1 with eccentric angles θ1 and θ2. Find the equation of the locus of the point of intersection of the tangents at P and Q if θ1 + θ2 = `π/2`.


Find the equations of the tangents to the ellipse `x^2/16 + y^2/9` = 1, making equal intercepts on co-ordinate axes


Select the correct option from the given alternatives:

If `"P"(pi/4)` is any point on he ellipse 9x2 + 25y2 = 225. S and S1 are its foci then SP.S1P =


Select the correct option from the given alternatives:

The equation of the tangent to the ellipse 4x2 + 9y2 = 36 which is perpendicular to the 3x + 4y = 17 is,


Find the equation of the ellipse in standard form if the length of major axis 10 and the distance between foci is 8


Answer the following:

Find the equation of the tangent to the ellipse x2 + 4y2 = 100 at (8, 3)


Let PQ be a focal chord of the parabola y2 = 4x such that it subtends an angle of `π/2` at the point (3, 0). Let the line segment PQ be also a focal chord of the ellipse E: `x^2/a^2 + y^2/b^2` = 1, a2 > b2. If e is the eccentricity of the ellipse E, then the value of `1/e^2` is equal to ______.


On the ellipse `x^2/8 + "y"^2/4` = 1 let P be a point in the second quadrant such that the tangent at P to the ellipse is perpendicular to the line x + 2y = 0. Let S and S' be the foci of the ellipse and e be its eccentricity. If A is the area of the triangle SPS' then, the value of (5 – e2). A is ______.


If the tangents on the ellipse 4x2 + y2 = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a2 is equal to ______.


If the chord through the points whose eccentric angles are α and β on the ellipse `x^2/a^2 + y^2/b^2` = 1 passes through the focus (ae, 0), then the value of tan `α/2 tan  β/2` will be ______.


Let the ellipse `x^2/a^2 + y^2/b^2` = 1 has latus sectum equal 8 units – if the ellipse passes through   `(sqrt(5), 4)` Then The radius of the directive circle is ______.


The points where the normals to the ellipse x2 + 3y2 = 37 are parallel to the line 6x – 5y = 2 are ______.


The normal to the ellipse `x^2/a^2 + y^2/b^2` = 1 at a point P(x1, y1) on it, meets the x-axis in G. PN is perpendicular to OX, where O is origin. Then value of ℓ(OG)/ℓ(ON) is ______.


Let the eccentricity of an ellipse `x^2/a^2 + y^2/b^2` = 1, a > b, be `1/4`. If this ellipse passes through the point ```(-4sqrt(2/5), 3)`, then a2 + b2 is equal to ______.


Eccentricity of ellipse `x^2/a^2 + y^2/b^2` = 1, if it passes through point (9, 5) and (12, 4) is ______.


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