Home
Class 12
MATHS
For the hyperbola 3x^(2) - 6y^(2) = - 18...

For the hyperbola `3x^(2) - 6y^(2) = - 18` find the length of transverse and conjugate axes and eccentricity .

Text Solution

Verified by Experts

The correct Answer is:
`sqrt3`
Promotional Banner

Topper's Solved these Questions

  • TWO DIMENSIONAL ANALYTICAL GEOMETRY - II

    SURA PUBLICATION|Exercise ( 5 marks )|5 Videos

  • TWO DIMENSIONAL ANALYTICAL GEOMETRY - II

    SURA PUBLICATION|Exercise (2 marks)|10 Videos

  • THEORY OF EQUATIONS

    SURA PUBLICATION|Exercise 4 MARKS|5 Videos

Similar Questions

Explore conceptually related problems

Statement 1 : The asymptotes of hyperbolas 3x+4y=2 and 4x-3y=5 are the bisectors of the transvers and conjugate axes of the hyperbolas. Statement 2 : The transverse and conjugate axes of the hyperbolas are the bisectors of the asymptotes.

If it is possible to draw the tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 having slope 2, then find its range of eccentricity.

If normal at P to a hyperbola of eccentricity 2 intersects its transverse and conjugate axes at Q and R, respectively, then prove that the locus of midpoint of QR is a hyperbola. Find the eccentricity of this hyperbola

If S_1a n dS_2 are the foci of the hyperbola whose length of the transverse axis is 4 and that of the conjugate axis is 6, and S_3a n dS_4 are the foci of the conjugate hyperbola, then the area of quadrilateral S_1S_3S_2S_4 is 24 (b) 26 (c) 22 (d) none of these

The foci a hyperbola coincides with the foci of the ellispe x^(2)/25 + y^(2)/9 = 1 . Find the equation of the hyperbola if its eccentricity is 2.

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

If asymptotes of hyperbola bisect the angles between the transverse axis and conjugate axis of hyperbola, then what is eccentricity of hyperbola?

If a hyperbola passes through the foci of the ellipse (x^2)/(25)+(y^2)/(16)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse and if the product of eccentricities of hyperbola and ellipse is 1 then the equation of hyperbola is (x^2)/9-(y^2)/(16)=1 b. the equation of hyperbola is (x^2)/9-(y^2)/(25)=1 c. focus of hyperbola is (5, 0) d. focus of hyperbola is (5sqrt(3),0)

Find the eccentricity of the hyperbola with foci on the x-axis if the length of its conjugate axis is (3/4)^("th") of the length of its tranverse axis.

Find the lengths of the transvers and the conjugate axis, eccentricity, the coordinates of foci, vertices, the lengths of latus racta, and the equations of the directrices of the following hyperbola: 16 x^2-9y^2=-144.