### Home > APCALC > Chapter 12 > Lesson 12.1.3 > Problem12-34

12-34.

Write the equation of the line tangent to the curve $x^{2}y - xy^{2} = 6$ at the point in the first quadrant where $y = 1$.

When $y = 1$, $x^{2} - x = 6$.
Therefore $x =$ ?

$2xy+x^2y^\prime-y^2-x(2y)y^\prime = 6$

Substitute the values of the coordinates of the point into the equation in Step 2. Then solve for $y′$.

Use the point from Step 1 and the slope ($y′$) from Step 3 to write the equation of the tangent line.