Vikas TU
Last Activity: 7 Years ago
Dear Student,
let hyperbola is x^2/a^2 – y^2/b^2 =1
P=(x1,y1)
S=(ae,0)=(sqrt(a^2+b^2),0)
ordinary at P is a^2*x/x1 + b^2*y/y1 = a^2+b^2
at G, y=0 so x=x1/a^2 (a^2+b^2)
LHS:SG=sqrt(a^2+b^2) – x1/a^2 (a^2+b^2)
SP=sqrt(sqrt(a^2+b^2)- x1)^2 +(- y1)^2)
RHS: eSP = e* sqrt(sqrt(a^2+b^2)- x1)^2 +(- y1)^2)
disentangling, we get sqrt(a^2+b^2) – x1/a^2 (a^2+b^2)=LHS
so LHS=RHS (consequently demonstrated)
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)
