हिंदी

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, - Mathematics and Statistics

Advertisements
Advertisements

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,

विकल्प

  • y = 4x + 6

  • 3y + 4x = 6

  • 3y = `4x + 6sqrt(5)`

  • 3y = x + 25

MCQ
Advertisements

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)`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Conic Sections - Miscellaneous Exercise 7 [पृष्ठ १७७]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 11 Maharashtra State Board
अध्याय 7 Conic Sections
Miscellaneous Exercise 7 | Q I. (16) | पृष्ठ १७७

संबंधित प्रश्न

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 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 eccentricity is `2/3` and passes through `(2, −5/3)`.


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


Show that the product of the lengths of the perpendicular segments drawn from the foci to any tangent line to the ellipse `x^2/25 + y^2/16` = 1 is equal to 16


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


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


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:

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


Select the correct option from the given alternatives:

The equation of the ellipse having eccentricity `sqrt(3)/2` and passing through (− 8, 3) is


Select the correct option from the given alternatives:

If the line 4x − 3y + k = 0 touches the ellipse 5x2 + 9y2 = 45 then the value of k 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


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 ______.


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 ______.


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 ______.


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


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×