Find the equations of the tangent and normal to the hyperbola at the point (x 0 , y 0 ).

Question

Philoid · Accepted Answer

It is given that the equations of the tangent and normal to the hyperbola , then,

On differentiating it with respect to x, we get,

Therefore, the slope of the tangent at (x₀, y₀) is

Then, the equation of the tangent at (x₀, y₀) is given by:

y - y₀ =

Then, slope of normal at (x₀, y₀)

=

Therefore, the equation of the normal at (x₀, y₀) is

y - y₀ = (x - x₀)

Therefore, the equation of the normal at (x₀, y₀) is.