MCQ
Equation $\sqrt {{{(x - 2)}^2} + {y^2}} + \sqrt {{{(x + 2)}^2} + {y^2}} = 4$ represents
- AParabola
- BEllipse
- CCircle
- ✓Pair of straight lines
✓
Answer
Correct option: D.
Pair of straight lines
d
(d) Given equation is , $\sqrt {{{(x - 2)}^2} + {y^2}} + \sqrt {{{(x + 2)}^2} + {y^2}} = 4$
$\sqrt {{{(x - 2)}^2} + {y^2}} = 4 - \sqrt {{{(x - 2)}^2} + {y^2}} $
(d) Given equation is , $\sqrt {{{(x - 2)}^2} + {y^2}} + \sqrt {{{(x + 2)}^2} + {y^2}} = 4$
$\sqrt {{{(x - 2)}^2} + {y^2}} = 4 - \sqrt {{{(x - 2)}^2} + {y^2}} $
Squaring both sides, we get $\sqrt {{{(x + 2)}^2} + {y^2}} = x + 2$
Again squaring both sides, we get ${y^2} = 0$, which is the equation of pair of straight lines.
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