chord `AB` of the circle `x^2+y^2=100` passes through the point `(7,1) ` and subtends are angle of `60^@` at the circumference of the circle. if `m_1` and `m_2` are slopes of two such chords then the value of `m_1*m_2` is

Options

A. `-1`
B. 1
C. `7//12`
D. `-3`

Answer

A

Explanation

Let theslope of the chord through point (7,1) be m. Thus, equation of line is
`y -1 = m(x-7)`
or `mx -y +1 -7m =0`
Perpendicular distanc from `(0,0) =(r )/(2)`
`rArr (|7-1|)/(sqrt(1+m^(2)))=5`
`rArr (7m -1)^(2) = 25 (1+m^(2))`
`rArr49m^(2) -14m +1 = 25 +25m^(2)`
`rArr 24 m^(2) -14m -24 =0`
`rArr m_(1)m_(2) =-1`