Question

If radius of director circle of auxiliary circle of ellipse $(3 x+4 y-1)^2+5(4 x-3 y+2)^2=250$ is $r$, then $[ r ]$ is equal to
[Note: $[ r ]$ denotes the greatest integer less than or equal to $r$.]

• A. 2
• B. 4
• C. 9
• D. 10

Answer 1

Answer: (B)

$\frac{(3 x+4 y-1)^2}{5}+5 \frac{(4 \times 3 y+2)^2}{5}=10$
$\frac{ P _1^2}{ a ^2}+\frac{ P _2^2}{ b ^2} $
$a ^2=10$
$b ^2=2$
Radius of auxiliary circle $=\sqrt{10}$
Hence, radius of director circle of auxiliary circle ' $r$ ' $=\sqrt{2} \cdot \sqrt{10}=\sqrt{20}$
$[ r ]=4$