I am preparing for an entrance exam and am focussing on co-ordinate geometry. However, one question has me stumbled:
If the line $\ell$ intersects the curve $\frac{y}2 = x^2 - 7$ at $(2,a)$ and $(1, b)$ then what is the slope of line $\ell$?
I am confused with the above equation and am having a hard time tackling this question. Any suggestions ?
HINT
Well, if the line $\ell$ intersects the curve $y/2 = x^2-7$ that means they share points, i.e., the intersection points lie both on the line and on the curve. You are told there are 2 such intersection points.
One of them is $(2,a)$, so is satisfies the curve and you must have $$ \frac{a}{2} = 2^2-7 \iff a = 2\left(2^2-7\right) = -6. $$
Can you continue?