Application of Derivatives
Shortest Distance
Premium Question
Grade 12
Question:
The shortest distance between the curve $y = x^2$ and the line $2x - y - 3 = 0$ is:
(1) $\frac{2\sqrt{5}}{5}$
(2) $\frac{3\sqrt{5}}{5}$
(3) $\frac{\sqrt{5}}{5}$
(4) $\sqrt{5}$
Step-by-Step Solution
Key Concept: Take a general point $(t, t^2)$ on the curve and write its (perpendicular) distance from the line as a function of $t$, then minimise that function.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)