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Select the correct option from the given alternatives: If P(π4) is any point on he ellipse 9x2 + 25y2 = 225. S and S1 are its foci then SP.S1P =

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प्रश्न

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 =

पर्याय

  • 13

  • 14

  • 17

  • 19

MCQ
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उत्तर

17

Explanation;

[Hint: SP·S'P = a2sin2θ + b2cos2θ, where 

a2 = 25, b2 = 9, θ = `pi/4`.]

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पाठ 7: Conic Sections - Miscellaneous Exercise 7 [पृष्ठ १७६]

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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. (8) | पृष्ठ १७६

संबंधित प्रश्‍न

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 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 latus rectum has length of 6 and foci are (±2, 0).


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 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 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


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


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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.


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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`.


Select the correct option from the given alternatives:

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


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 ______.


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 ______.


Tangents are drawn from a point on the circle x2 + y2 = 25 to the ellipse 9x2 + 16y2 – 144 = 0 then find the angle between the tangents.


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 ______.


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 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______.


\[\frac{x^{2}}{r^{2}-r-6}+\frac{y^{2}}{r^{2}-6r+5}=1\] will represent the ellipse, if r lies in the interval______.


Eccentricity of the conic \[16x^2+7y^2=112\] is______.


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


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