Tangent to the curve

• Apr 20th 2008, 04:10 AM
mx-
Tangent to the curve
Consider the curve given by $2xy - \sqrt{x^2+y}=-23$.
Find the equation of the line tangent to the curve at the point (−2, 5)

Thanks
• Apr 20th 2008, 04:25 AM
Mathstud28
Quote:

Originally Posted by mx-
Consider the curve given by $2xy - \sqrt{x^2+y}=-23$.
Find the equation of the line tangent to the curve at the point (−2, 5)

Thanks

Differentiating implicitly we get $2xy'+2y-\frac{1}{2}(x+2y)^{\frac{-1}{2}}\cdot(2x+y')=0$ now using this we get $y-5=f'(-2,5)(x+2)$ I will leave the evaluation of f'(-2,5) to you...plug it in and solve for y'