Q206 / 270 · NDA 2021 (Phase 1) · Mathematics

What is the radius of the circle $4 x^2+4 y^2-20 x+12 y-15$ $=0$ ?

  • A
    14 units
  • B
    10.5 units
  • C
    7 units
  • Correct answer
    D
    3.5 units

Solution

Circle equation : $\begin{aligned} & 4 x^2+4 y^2-20 x+12 y-15=0 \\ & \Rightarrow x^2+y^2-5 x+3 y-\frac{15}{4}=0 \\ & \text { Radius }=\sqrt{(-g)^2+(-f)^2-C} \end{aligned}$ Here, $g=-\frac{5}{2}, f=\frac{3}{2}$ and $C=-\frac{15}{4}$ $\begin{aligned} \therefore \text { Radius } & =\sqrt{\left(\frac{5}{2}\right)^2+\left(-\frac{3}{2}\right)^2-\left(-\frac{15}{4}\right)} \\ & =\sqrt{\frac{25+9+15}{4}}=\frac{7}{2}=3.5 \text { units. } \end{aligned}$

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

Relevant Questions