Question

The curve $y=\frac{x^2}{2}$ and the line $y=\frac{x}{2}$ intersect at the origin and at the point $(a,b)$, as shown in the figure above. Find the value of $b$.

• A. $\frac{1}{8}$
• B. $\frac{1}{4}$
• C. $\frac{1}{2}$
• D. $1$
• E. $2$

Answer 1

The correct option is C $\frac{1}{2}$

To determine where two curves intersect, set the equations equal to one another and solve for $x$.
We need to figure out which values of $x$ satisfy:
$\Rightarrow$ $\frac{x^2}{2}=\frac{x}{2}$
Dividing both sides by $x$, we get $x=1$.
As the question asking for $y$-axis point $b$ so, we can put the obtained value of $x$ in any of the equation. Plugging the value of $x=1$ in $y=\frac{x}{2}$, we get $y=\frac{1}{2}$.
Hence, option C is correct.