Question

If line y = 2x + c neither cuts the circle $(x–2{)}^2+(y–3{)}^2=4$ nor the ellipse $x^2+6y^2=6$, then the range of c is

• A. [-5, 5]
• B. $(-\infty ,-5)\cup (5,\infty )$
• C. (-4, 4)
• D. (-3, 3)

Answer 1

The correct option is B

$(-\infty ,-5)\cup (5,\infty )$

Since the given line does not meet the given ellipse and circle.
$c^2>6\times 2^2+1[From{c}^2>a^2{m}^2+b^2]and{c}^2>4(1+4)[From{c}^2>a^2(1+m^2\left)\right]\Rightarrow c^2>25\therefore cϵ(-\infty ,-5)\cup (5,\infty )$