Obtain the equations of the straight lines passing through the point A(2, 0) & making 45 with the tangent at A to the circle `(x + 2)^2 + (y-3)^2 = 25`. Find the equations of the circles each of radius 3 whose centres are on these straight lines at a distance of `5sqrt2` from A.

Options

A. `(x-1)^(2)+(y-7)^(2)=9`
B. `(x-3)^(2)+(y+7)^(2)=9`
C. `(x-9)^(2)+(y-1)^(2)=9`
D. `(x+9)^(2)+(y+1)^(2)=9`

Answer

A, B, C, D

Explanation

Equation of tangent at `A` is `4x-3y-8=0`
Let `y=m(x-2)` in line thro `(2,0)` and `m=-7` or `1/7`
We have `(x-2)/(- 1/(sqrt(50)))=y/(7/(sqrt(50)))=5sqrt(2)`
`implies` Centre of circle are `(1,7), (3,-7),(9,1)` and `d(-5,-1)`