Question #53c2f

1 Answer
Ratnaker Mehta
Jun 25, 2016

#sqrt2x-y-1=0.#

Explanation:

Eqn. of Hyperbola : #x^2-y^2=1.#

Diff. both sides w.r.t. #x, 2x-2ydy/dx=0.#
#:. dy/dx=x/y, y!=0.#
#:.[dy/dx]_(x=sqrt2,y=1) = sqrt2.#
#:.# Slope of tgt. to Hyp. at pt. # (sqrt2,1)=sqrt2,# & pt. #(sqrt2,1)# is on the tgt.

Hence, reqd. eqn. of tgt. is #: y-1=sqrt2*(x-sqrt2),# writing it in std. form, #sqrt2x-y-1=0.#

Here, we had to find the eqn. of tgt. using implicit diffn. Otherwise, eqn. of the tgt. line at a pt.#(h,k)# on Hyp. : #x^2-y^2=1,# is, #hx-ky=1.#

Here, pt. #(h,k)=(sqrt2,1)# is on Hyp. #: x^2-y^2=1,# since it satisfy the eqn. of Hyp.So, tgt.line is #sqrt2x-y=1,# as before!

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