Question

The set of values of 'c' so that the equations $y=\left|x\right|+cand{x}^2+y^2-8\left|x\right|-9=0$ have no solution is

• A. $(\infty ,-3)\cup (3,\infty )$
  
• B. $(-3,3)$
  
• C. $(-\infty ,5\sqrt{2})\cup \left(5\sqrt{(}2\right),\infty )$
  
• D. $5\sqrt{2}-4,\infty$

Answer 1

The correct option is D

$5\sqrt{2}-4,\infty$

Since $y=\left|x\right|+cand{x}^2+y^2-8\left|x\right|-9=0$ both are symmetrically about y-axis for x>0, y=x+c.
Equation of tangent to circle $x^2+y^2-8x-9=0$ parallel to y=x+c is $y=(x-4)+5\sqrt{1+1}$
$\Rightarrow y=x+(5\sqrt{2}-4)$
For no solution c>$5\sqrt{2}-4$
$\therefore cϵ(5\sqrt{2}-4,\infty )$