Question

If a variable line y = 2x + p lies between the circles $x^2+y^2-2x-2y+1=0$ and $x^2+y^2-16x-2y+61=0$ without intersecting or touching either circles, then number of integral values of p is

• A. 9
• B. 8
• C. 7
• D. 6

Answer 1

The correct option is C 7

$C_1=(1,1)$ $C_2=(8,1)$
$r_1=1$
$r_2=2$
let L = 2x – y + P = 0
$L_{11}{L}_{22}$ < 0 $(1+p)(15+p)$ <0 ......(1)
$\frac{|1+p|}{\sqrt{5}}$ > 1.....(2)
$\frac{|15+p|}{\sqrt{5}}$ >2 .....(3)