Q91 / 160 · AP EAMCET 2018 (24 Apr Shift 1) · Mathematics

The number of common tangents to the circles $x^2+y^2-4 x-2 y+k=0$ and $x^2+y^2-6 x-4 y+l=0$, having radii 2 and 3 respectively, is

  • A
    4
  • Correct answer
    B
    2
  • C
    3
  • D
    1

Solution

Given circle are, $$ \begin{gathered} x^2+y^2-4 x-2 y+k=0 \\ \therefore \quad \text { Centre } c_1(2,1) \text { and } r_1=2 \\ \quad x^2+y^2-6 x-4 y+l=0 \end{gathered} $$ Centre $c_2(3,2)$ and $r_2=3$ $$ \begin{aligned} c_1 c_2 & =\sqrt{(2-3)^2+(1-2)^2} \\ & =\sqrt{1+1}=\sqrt{2} \\ c_1 c_2 & < r_1+r_2 \end{aligned} $$ So, circles have two common tangents.

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

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