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Select the correct option from the given alternatives: If the line 2x − y = 4 touches the hyperbola 4x2 − 3y2 = 24, the point of contact is - Mathematics and Statistics

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प्रश्न

Select the correct option from the given alternatives:

If the line 2x − y = 4 touches the hyperbola 4x2 − 3y2 = 24, the point of contact is

पर्याय

  • (1, 2)

  • (2, 3)

  • (3, 2)

  • (−2, −3)

MCQ

उत्तर

If the line 2x − y = 4 touches the hyperbola 4x2 − 3y2 = 24, the point of contact is (3, 2)

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Conic Sections - Hyperbola
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Conic Sections - Miscellaneous Exercise 7 [पृष्ठ १७७]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board
पाठ 7 Conic Sections
Miscellaneous Exercise 7 | Q I. (19) | पृष्ठ १७७

संबंधित प्रश्‍न

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`x^2/25 - y^2/16` = 1


Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`x^2/25 - y^2/16` = – 1


Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

16x2 – 9y2 = 144


Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`y^2/25 - x^2/144` = 1


Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`x^2/100 - y^2/25` = + 1


Find the eccentricity of the hyperbola, which is conjugate to the hyperbola x2 – 3y2 = 3


If e and e' are the eccentricities of a hyperbola and its conjugate hyperbola respectively, prove that `1/"e"^2 + 1/("e""'")^2` = 1


Find the equation of the hyperbola referred to its principal axes:

whose length of conjugate axis = 12 and passing through (1, – 2)


Find the equation of the hyperbola referred to its principal axes:

which passes through the points (6, 9) and (3, 0)


Find the equation of the hyperbola referred to its principal axes:

whose vertices are (± 7, 0) and end points of conjugate axis are (0, ±3)


Find the equation of the hyperbola referred to its principal axes:

whose foci are at (±2, 0) and eccentricity `3/2`


Find the equation of the hyperbola referred to its principal axes:

whose length of transverse and conjugate axis are 6 and 9 respectively


Find the equation of the hyperbola referred to its principal axes:

whose length of transverse axis is 8 and distance between foci is 10


Find the equation of the tangent to the hyperbola:

3x2 – 4y2 = 12 at the point (4, 3)


Find the equation of the tangent to the hyperbola:

9x2 – 16y2 = 144 at the point L of latus rectum in the first quadrant


Find the equations of the tangents to the hyperbola `x^2/25 - y^2/9` = 1 making equal intercepts on the co-ordinate axes


Find the equations of the tangents to the hyperbola 5x2 – 4y2 = 20 which are parallel to the line 3x + 2y + 12 = 0


Select the correct option from the given alternatives:

Eccentricity of the hyperbola 16x2 − 3y2 − 32x − 12y − 44 = 0 is


Answer the following:

For the hyperbola `x^2/100−y^2/25` = 1, prove that SA. S'A = 25, where S and S' are the foci and A is the vertex


Answer the following:

Find the equation of the hyperbola in the standard form if eccentricity is `3/2` and distance between foci is 12.


Answer the following:

Find the equation of the tangent to the hyperbola x = 3 secθ, y = 5 tanθ at θ = `pi/3`


Answer the following:

Find the equation of the tangent to the hyperbola `x^2/25 − y^2/16` = 1 at P(30°)


Answer the following:

Find the equations of the tangents to the hyperbola 3x2 − y2 = 48 which are perpendicular to the line x + 2y − 7 = 0


The eccentricity of the hyperbola 25x2 - 9y2 = 225 is ______.


The foci of a hyperbola coincide with the foci of the ellipse `x^2/25 + y^2/9` = 1. Find the equation of the hyperbola, if its eccentricity is 2.


Parametric form of the hyperbola `x^2/4 - y^2/9` = –1 is ______.


The hyperbola `x^2/a^2 - y^2/b^2` = 1 passes through the point of intersection of the lines `x - 3sqrt(5)y` = 0 and `sqrt(5)x - 2y` = 13 and the length of its latus rectum is `4/3` units. The coordinates of its focus are ______.


The equation of conjugate axis for the hyperbola `(x + y + 1)^2/4 - (x - y + 2)^2/9` = 1 is ______.


The number of points from where a pair of perpendicular tangents can be drawn to the hyperbola, x2sec2α – y2cosec2α = 1, `α∈(0, π/4)` are ______.


Let the hyperbola H : `x^2/a^2 - y^2/b^2` = 1 pass `(2sqrt(2), -2sqrt(2))`. A parabola is drawn whose focus is same as the focus of H with positive abscissa and the directrix of the parabola passes through the other focus of H. If the length of the latus rectum of the parabola is e times the length of the latus rectum of H, where e is the eccentricity of H, then which of the following points lies on the parabola?


Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola `x^2/"a"^2 - "y"^2/"b"^2` = 1. Let e' and l' respectively the eccentricity and length of the latus rectum of its conjugate hyperbola. If e2 = `11/14"l'"` and (e')2 = `11/8"l"^'` then the value of 77a + 44b is equal to ______.


The hyperbola `x^2/a^2 - y^2/b^2` = 1 passes through the point `(3sqrt(5), 1)` and the length of its latus rectum is `4/3` units. The length of the conjugate axis is ______.


The eccentricity of the hyperbola x2 – 3y2 = 2x + 8 is ______.


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