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CONIC SECTIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSCONIC SECTIONS1 Mark
MCQ
The equation $\sqrt{(\text{x}-2)^{2}+\text{y}^{2}}+\sqrt{(\text{x}+2)^{2}+\text{y}^{2}}=5$ represents:
  • A
    A circle
  • ✓
    Ellipse
  • C
    Line segment
  • D
    An empty set
✓

Answer

Correct option: B.
Ellipse
let A (2, 0), B (-2, 0) and P (x, y) be three points AB = 4
Given: that, $\sqrt{(\text{x}-2)^{2}+\text{y}^{2}}+\sqrt{(\text{x}+2)^{2}+\text{y}^{2}}=5>\text{AB}$
⇒ PA + PB = constant > AB
$\therefore$ locus of P is an ellipse.

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