A solid regular right circular cylinder is sliced by a flat plane that does not pass through the bases and is tilted at an acute angle to the cylinder's longitudinal axis. The geometric shape of the cross-section formed on the cutting plane is:

(A) An ellipse

(B) A circle

(C) A parabola

(D) A hyperbola

Answer Key:

Verified in official key

### 1. Strategy & Theoretical Principles In 3D solid geometry and conic sections: - Slicing a right circular cylinder perpendicular to its axis creates a **circle**. - Slicing a right circular cylinder with a plane inclined at an angle to its axis that cuts completely across both opposite side generators creates an **ellipse**. - Slicing parallel to the cylinder axis creates two parallel straight lines (or a rectangle). ### 2. Distractor Forensics - Parabolas and hyperbolas can be formed by slicing a *cone*, but slicing an infinitely long or bounded cylinder never produces a parabola or hyperbola. ### 3. Exam Trap & Standard Reference - **Trap Alert:** In a cylinder (unlike a cone), inclined cross-sections that cut across the cylinder are always strictly elliptical. - **Standard Reference:** GATE General Aptitude Official Syllabus - Spatial Aptitude.

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