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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,

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प्रश्न

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,

पर्याय

  • y = 4x + 6

  • 3y + 4x = 6

  • 3y = `4x + 6sqrt(5)`

  • 3y = x + 25

MCQ
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उत्तर

The equation of the tangent to the ellipse 4x2 + 9y2 = 36 which is perpendicular to the 3x + 4y = 17 is, 3y = `4x + 6sqrt(5)`

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

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बालभारती Mathematics and Statistics (Arts and Science) Part 1 [English] Standard 11 Maharashtra State Board
पाठ 7 Conic Sections
Miscellaneous Exercise 7 | Q I. (16) | 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 equation of the ellipse in standard form if eccentricity = `3/8` and distance between its foci = 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 passing through the points (−3, 1) and (2, −2)


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


Find the eccentricity of an ellipse if the distance between its directrix is three times the distance between its foci


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


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 5x2 + 9y2 = 45 which are ⊥ to the line 3x + 2y + y = 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


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:

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


Select the correct option from the given alternatives:

Centre of the ellipse 9x2 + 5y2 − 36x − 50y − 164 = 0 is at


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


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 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 ______.


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 ______.


The point on the ellipse x2 + 2y2 = 6 closest to the line x + y = 7 is (a, b). The value of (a + b) will be ______.


The ratio of the area of the ellipse and the area enclosed by the locus of mid-point of PS where P is any point on the ellipse and S is the focus of the ellipse, is equal to ______.


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 ______.


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 ______.


The locus of a variable point whose distance from (- 2, 0) is \[\frac{2}{3}\] times its distance from the line \[x=-\frac{9}{2}\], 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 between the foci of the ellipse \[x=3\text{cos}\theta,y=4\text{sin}\theta\] is______.


The distance between the foci of the ellipse \[3x^2+4y^2=48\] is______.


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


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