If the line y = 7x - 25 meets the circle `x^(2) + y^(2) = 25` in the points A,B then the distance between A and B is

Options

A. `sqrt10`
B. 10
C. `5sqrt2`
D. 5

Answer

C

Explanation

The intersection point of line y=7x-25 and cricle `x^(2)+y^(2)=25`is` x^(2)+(7x-25)^(2)=25.`
`rArr" " 50x^(2)-350x+600=0 `
` rArr" " (x-3)(x-4)=0`
` rArr" " x=3,x=4rArry=-4,3 so, coordinates are a(3,-4) and b( 4,3). `therefore` distance between a and b = `(sqrt((4-3^(2))+(3+4^(2)))`=5sqrt2 required distance `=2sqrt(a^(2)1+m^(2))/(1+m2)`
`=2sqrt(25(1+49)-625)/(1+49)=5sqrt2`