The equation of a tangent to the hyperbola 4x2 -- 5y2 = 20 parallel to the line x -- y = 2…

Question

The equation of a tangent to the hyperbola 4x2 -- 5y2 = 20 parallel to the line x -- y = 2 is :

Accepted Answer

Hyperbola $${{{x^2}} \over 5} - {{{y^2}} \over 4} = 1$$

slope of tangent = 1

equation of tangent y = x $$ \pm $$ $$\sqrt {5 - 4} $$

$$ \Rightarrow $$  y = x $$ \pm $$ 1

$$ \Rightarrow $$  y = x + 1

or

$$ \Rightarrow $$  y = x - 1

Solutions · 1