Let `xa n dy` be real variables satisfying `x^2+y^2+8x-10 y-40=0` . Let `a=max{sqrt((x+2)^2+(y-3)^2)}` and `b=min{sqrt((x+2)^2+(y-3)^2)}` . Then (a)`a+b=18` (b) `a+b=sqrt(2)` (c) `a-b=4sqrt(2)` (d) `adotb=73`

Options

A. `a+b=18`
B. `a+b=sqrt(2)`
C. `a-b=4sqrt(2)`
D. `a.b=72`

Answer

1,3,4

Explanation

`x^(2)+y^(2)+8x-10y-40=0`
The center of the circle is `(-4,5)`.
its radius is 9. distance of the center `(-4,5)` from the point `(-2,3)` is `sqrt(4+4)=2sqrt(2)`. Therefore, `a=2sqrt(2)+9` and `b= -2sqrt(2) +9`
`:. a+b=18`
`a-b=18`
`a-b=4sqrt(2)`
`a.b =81-8=73`