Question

Find the equations of tangent to the hyperbola 3x^2-4y^2=12 which make equal intercepts on the axes

Answer 1

Thank you for asking this question. Here is your answer:

x²/ 4 - y²/3 = 1 ⇒a² = 4, b² = 3

x/k + y/k = 1 or x + y = k or y = - x + k

⇒  m = -1 and c = k

Now k² = a² m² - b²

= 4(-1)² - 3

= 4-3

= 1

⇒ k = + - 1

So the equation of the tangents are: x + y = + - or x + y + - = 0

it can also be taken as  x - y = k

Then k  = + - 1 and  x - y = + - 1

or x - y +-1 = 0

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