Doubt from hyperbola

Is equation of tangent with slope m is little different for shifted hyperbola whose center is (h,k) ? from standard hyperbola

No just replace x with x-h and y with y-k

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Exercise 2 third part

Exercise 3 vth part

Question 5 i am getting beta^2=2alpha^2-10 not 7 please check it

In question 10 shouldn't be intercept of unit length not given length

Question no 11 too