transverse axis of a hyperbola is of length 2a and a vertex dvides the segment of the axis between the - Maths - Conic Sections

Question

transverse axis of a hyperbola is of length 2a and a vertex dvides
the segment of the axis between the centre and the corresponding
focus in ratio 2:1, then the equation of hyperbola is?
( Ans 5x^2 -4y^2 = 5a^2 )

Neha Sethi · Accepted Answer

Dear student
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5a17c35fe40e3%20png">
Clearly, 2ae3=a⇒e=32So, S=3a2,0Directrix is x=ae=a32=2a3So, eq of hyperbola will be x-3a22+y2=94x-2a32x2+9a24-3ax+y2=94x2+4a29-4ax3x2+9a24-3ax+y2=9x24+a2-3ax4x2+9a2+4y2=9x2+4a25x2-4y2=5a2
Regards

transverse axis of a hyperbola is of length 2a and a vertex dvides the segment of the axis between the centre and the corresponding focus in ratio 2:1, then the equation of hyperbola is? ( Ans. 5x^2 -4y^2 = 5a^2 )

transverse axis of a hyperbola is of length 2a and a vertex dvides the segment of the axis between the centre and the corresponding focus in ratio 2:1, then the equation of hyperbola is?
( Ans. 5x^2 -4y^2 = 5a^2 )