Question

Let \(a\) and \(b\) be the distances from the point \((2,3,4)\) to the XY plane and Y-Axis respectively. Then \(a^{2}+b^{2}=\)

• A. \(10\)
• B. \(29\)
• C. \(22\)
• D. \(36\)

Hint:

The distance from the XY plane is the absolute z-coordinate; the distance from the Y-axis uses x and z.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For a point \((x,y,z)\), the distance from the XY plane is \(|z|\) and the distance from the Y-axis is \(\sqrt{x^{2}+z^{2}}\).

Step 2: Distance a
For \((2,3,4)\), \(a=4\), so \(a^{2}=16\).

Step 3: Distance b
\(b=\sqrt{2^{2}+4^{2}}=\sqrt{20}\), so \(b^{2}=20\).

Step 4: Add
\(a^{2}+b^{2}=16+20=36\).

Final Answer:
The value of a squared plus b squared is 36. \[ \boxed{\text{(D) }36} \]