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Conic Sections — Maths STD 11 Science — Question

CBSE 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, $\sqrt{(\text{x}-2)^{2}+\text{y}^{2}}+\sqrt{(\text{x}+2)^{2}+\text{y}^{2}}=5>\text{AB}$
$\Rightarrow PA + PB =$ constant $> AB$
$\therefore$ locus of $P$ is an ellipse.

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