equation of the lines.

Question

find the equations for the tangent lines, to the hyperbola y^2/4 - x^2/2 = 1.

Answer 1

The hyperbola is .

Differentiating the above equation.

Slope (m) =

The equation of tangent line is 

Answer 2

The hyperbola is .

Differentiating the above equation.

Slope (m) = 

 

Find the slope at (x1, y1) which is intersection point of the curve and tangent line.

m = 2x1/y1

The equation of tangent line is  

The tangent line equation is y - y1 = 2x1/y1 (x - x1)

yy1 - y1^2 = 2xx1 - 2x1^2

2xx1 - yy1 - 2x^2 + y1^2 = 0