Q237 / 270 · NDA 2023 (Phase 2) · Mathematics

Consider the following in respect of the circle $4 x^2+4 y^2-4 a x-4 a y+a^2=0$ : 1. The circle touches both the axes. 2. The diameter of the circle is 2 a . 3. The centre of the circle lies on the line $x+y=a$. How many of the statements given above are correct

  • A
    Only one
  • Correct answer
    B
    Only two
  • C
    All three
  • D
    None

Solution

Given, $4 x^2+4 y^2-4 a x-4 a y+a^2=0$ $\Rightarrow\left(x-\frac{a}{2}\right)^2+\left(y-\frac{a}{2}\right)^2=\left(\frac{a}{2}\right)^2$ So, this circle touches both the axis, Diameter of circle $=\frac{\mathrm{a}}{2}+\frac{\mathrm{a}}{2}=\mathrm{a}$ and the centre lies on the line $x+y=a$

Hence, the correct answer is option: 'B'.

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