Application of Derivatives
Tangents and Normals
Premium Question
Grade 12
Question:
The tangent at any point on the curve $\sqrt{x} + \sqrt{y} = \sqrt{a}$ cuts the coordinate axes at points whose sum of intercepts equals:
(1) $a$
(2) $2a$
(3) $\sqrt{a}$
(4) $\frac{a}{2}$
Step-by-Step Solution
Key Concept: Differentiate $\sqrt{x} + \sqrt{y} = \sqrt{a}$ implicitly to obtain the slope at a general point on the curve, then write the tangent line and find where it meets each axis.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)