find eq of hyperbola passing (2 8) with respect to hyperbola 5 x square minus y square equal to 5
Greetings Aspirant,
The Answer to your question is as follow:
Let the equation of the tangent be
y=mx+c
Since it passes through (2,8) hence
8=2m+c
Or
c=8−2m
Hence the equation of the tangent becomes
y=mx−2m+8
Substituting in the equation of the hyperbola
5x(Square) −y(Square) =5
5x(Square) − (mx−2m+8)(Square) = 5
5x(Square)−5−(m(Square)x(Square)+4m(Square)+64−4m(Square)x−32m+16mx)=0
x(Square)(5−m(Square) )+x(4m(Square) −16m)−4m(Square) +32m−69=0
Since it is a tangent hence D is 0.
Or
B(Square) −4AC=0
(4m(Square) −16m)(Square) −4(5−m(Square) ) (−4m(Square) +32m−69)=0
m=3 and m=23/3
Hence
y=3x+2 and 3y=23x−22
For Your Better Understanding i have also uploaded an image of the same answer to your question. You may go through it.
Answer Image (https://drive.google.com/drive/folders/17Q4BTcoBKGmANQIhhdKF_5ZZkJcqGWAP?usp=sharing)
Hope My Answer Helped You.
Best of Luck For Future.
