$\"\"$

The equation of hyperbola is $\"\"$ .

At the point $\"\"$ the hyperbola equation is $\"\"$ .

Slope of the tangent is derivative of the function at a particular point.

Find the derivative of the curve.

Consider $\"\"$ .

Differentiate on each side with respect to $\"\"$ .

$\"\"$

Slope of the tangent line at the point $\"\"$ is $\"\"$ .

Find the equation of the tangent line.

Point-slope form of line equation: $\"\"$ .

Substitute $\"\"$ and $\"\"$ in point-slope formula.

$\"\"$

Substitute $\"\"$ in the above equation.

$\"\"$

Equation of a tangent line is $\"\"$ .

The equation of a tangent line is $\"\"$ .