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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Ellipse

NDA 2018 · Mathematics · Ellipse

The second degree equation x^2+4 y-2 x-4 y+2=0 represents

The second degree equation x2+4y−2x−4y+2=0x^2+4 y-2 x-4 y+2=0 represents

Options

  1. AA point
  2. BAn ellipse of semi-major axis 1
  3. CAn ellipse with eccentricity \frac{\sqrt{3}}{2}
  4. DNone of the above

Correct answer

A. A point

Step-by-step solution

∵(x2−2x+1)+(4y2−4y+1)=0⇒(x−1)2+(2y−1)2=0⇒x=1,y=12\begin{array}{ll} \because & \left(x^2-2 x+1\right)+\left(4 y^2-4 y+1\right)=0 \\ \Rightarrow & (x-1)^2+(2 y-1)^2=0 \\ \Rightarrow & x=1, y=\frac{1}{2} \end{array} It is a point.
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