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Select the correct option from the given alternatives: The equation of the ellipse is 16x2 + 25y2 = 400. The equations of the tangents making an angle of 180° with the major axis are - Mathematics and Statistics

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प्रश्न

Select the correct option from the given alternatives:

The equation of the ellipse is 16x2 + 25y2 = 400. The equations of the tangents making an angle of 180° with the major axis are

विकल्प

  • x = 4

  • y = ± 4

  • x = – 4

  • x = ± 5

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उत्तर

The equation of the ellipse is 16x2 + 25y2 = 400. The equations of the tangents making an angle of 180° with the major axis are y = ± 4

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अध्याय 7: Conic Sections - Miscellaneous Exercise 7 [पृष्ठ १७७]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 11 Maharashtra State Board
अध्याय 7 Conic Sections
Miscellaneous Exercise 7 | Q I. (15) | 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:

3x2 + 4y2 = 12


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 equation of the ellipse in standard form if the distance between directrix is 18 and eccentricity is `1/3`.


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)`.


Find the eccentricity of an ellipse, if the length of its latus rectum is one-third of its minor axis.


Find the equation of the tangent to the ellipse `x^2/5 + y^2/4` = 1 passing through the point (2, –2)


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 x2 + 4y2 = 9 which are parallel to the line 2x + 3y – 5 = 0.


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.


Find the equation of the tangent to the ellipse 5x2 + 9y2 = 45 which are ⊥ to the line 3x + 2y + y = 0.


Find the equation of the locus of a point the tangents form which to the ellipse 3x2 + 5y2 = 15 are at right angles


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


The eccentric angles of two points P and Q the ellipse 4x2 + y2 = 4 differ by `(2pi)/3`. Show that the locus of the point of intersection of the tangents at P and Q is the ellipse 4x2 + y2 = 16


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


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 ______.


The tangent and the normal at a point P on an ellipse `x^2/a^2 + y^2/b^2` = 1 meet its major axis in T and T' so that TT' = a then e2cos2θ + cosθ (where e is the eccentricity of the ellipse) is equal to ______.


An ellipse is described by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the necessary length of the string and the distance between the pins respectively in cms, are ______.


The eccentricity, foci and the length of the latus rectum of the ellipse x2 + 4y2 + 8y – 2x + 1 = 0 are respectively equal to ______.


The equation of the ellipse with its centre at (1, 2), one focus at (6, 2) and passing through the point (4, 6) is ______.


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 ______.


If P1 and P2 are two points on the ellipse `x^2/4 + y^2` = 1 at which the tangents are parallel to the chord joining the points (0, 1) and (2, 0), then the distance between P1 and P2 is ______.


A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is `1/2`. Then the length of the semi-major axis is ______.


If the length of the major axis of the ellipse \[\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\] is three times the length of minor axis, then its eccentricity is______.


The distance of the point \[^{\prime}\theta^{\prime}\] on the ellipse \[\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\] from a focus is______.


For the ellipse \[3x^2+4y^2=12,\] the length of latus rectum is______.


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