find the equation of hyperbola in standard form having  distance between directrices is  4/3 root3  and passing through point (2,1)????????

Dear Student,
Please find below the solution to the asked query:

Standard equation of hyperbola is:x2a2-y2b2=1As it passes through 2,1. Hence4a2-1b2=1 4a2-1=1b24-a2a2=1b2b2=a24-a2 ;iDistance between directrices=4332ae=4334a2e2=16×39a2e2=43 iiAlsoe2=a2+b2a2a2+b2=a2e2a2+b2=43 Using iia2+a24-a2=43 Using i4a2-a4+a24-a2=435a2-a44-a2=4315a2-3a4=16-4a23a4-19a2+16=03a4-3a2-16a2+16=03a2a2-1-16a2-1=0a2-13a2-1=0a2=1 or a2=13When a2=1 b2=14-1=13Hence equation will be:x21-y213=1x2-3y2=1When a2=13b2=134-13b2=111Hence equation will be:x213-y2111=13x2-11y2=1

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.

  • -11
What are you looking for?