If the equation of the circle whose radius is 3 units and which touches internally the circle $x^2+y^2-4 x-6…

If the equation of the circle whose radius is 3 units and which touches internally the circle $x^2+y^2-4 x-6 y-12$ $=0$ at the point $(-1,-1)$ is $x^2+y^2+p x+q y+r=0$, then $p+q-r=$
  1. 2
  2. $\frac{5}{2}$
  3. $\frac{26}{5}$
  4. 3

Solution

$x^2+y^2+p x+q y+r=0$ touches the given circle at $(-1,-1)$. Hence $(-1)^2+(-1)^2-p-q+r=0$ $\Rightarrow p+q-r=2$.

Asked in: AP EAMCET 2024 (21 May Shift 2)

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