English

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

Advertisements
Advertisements

Question

Select the correct option from the given alternatives:

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

Options

  • 9x2 + 16y2 = 144

  • 144x2 + 9y2 = 1296

  • 128x2 + 144y2 = 18432

  • 144x2 + 128y2 = 18432

MCQ

Solution

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

shaalaa.com
Conic Sections - Ellipse
  Is there an error in this question or solution?
Chapter 7: Conic Sections - Miscellaneous Exercise 7 [Page 177]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board
Chapter 7 Conic Sections
Miscellaneous Exercise 7 | Q I. (12) | Page 177

RELATED QUESTIONS

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 eccentricity = `3/8` and distance between its foci = 6


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 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 x – y = 5 is a tangent to the ellipse 9x2 + 16y2 = 144. 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 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.


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 eccentricity `sqrt(3)/2` and passing through (− 8, 3) is


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


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)


The length of the latusrectum of an ellipse is `18/5` and eccentncity is `4/5`, then equation of the ellipse is ______.


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 ______.


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 ______.


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 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 ______.


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


Equation of the ellipse whose axes are along the coordinate axes, vertices are (± 5, 0) and foci at (± 4, 0) 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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×