Q12 of 292 Page 564

Show that the equation of the tangent to the hyperbola at is .

At (x₁, y₁) : ⇒ b²x₁² – a²y₁² = a²b²

y – b = m(x – a)

a²y₁y – a²y₁² = b²x₁x – b²x₁²

b²x₁x – a²y₁y = a²b²

Find the equations of the tangent and the normal to the given curve at the indicated point for

at the point where x = 1

Find the equation of the tangent to the curve

Find the equation of the tangent to the curve .

Find the equation of the normal to the curve