हिंदी

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 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • + 21

  • `± 3sqrt(21)`

  • + 3

  • + 3(21)

MCQ
Advertisements

उत्तर

If the line 4x − 3y + k = 0 touches the ellipse 5x2 + 9y2 = 45 then the value of k is `± 3sqrt(21)`

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. (14) | पृष्ठ १७७

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:

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 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 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.


Show that the line x – y = 5 is a tangent to the ellipse 9x2 + 16y2 = 144. Find the point of contact


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 `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 x2 + 4y2 = 20, ⊥ to the line 4x + 3y = 7.


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`.


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


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 =


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:

The equation of the tangent to the ellipse 4x2 + 9y2 = 36 which is perpendicular to the 3x + 4y = 17 is,


Select the correct option from the given alternatives:

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


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 ______.


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 ______.


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 ______.


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 ______.


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 ______.


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 ______.


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


Length of latusrectum of the ellipse \[\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1,\] is______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×