Well for part (a) since the equation of a slope is $\displaystyle \frac{y_2-y_1}{x_2-x_1}$ then the expression should be $\displaystyle \frac{a^2-x^2}{a-x}$ right?You can find the slope of thetangent lineto a parabola $\displaystyle y=x^2$ at a point $\displaystyle P(a,a^2)$ using the following method.

(a) Find an expression, in terms of x and a, for the slope of asecant linefrom $\displaystyle P$ to another point $\displaystyle Q(x,x^2)$ on the parabola.

(b) Simplify this slope assuming $\displaystyle x \not= a$. What number, in terms of $\displaystyle a$, does this quantity approach as $\displaystyle x$ approaches $\displaystyle a$?

I don't understand part (b) at all.