Question

If values of a, for which the line `y=ax+2sqrt(5)` touches the hyperbola `16x^2-9y^2 = 144` are the roots of the equation `x^2-(a_1+b_1)x-4=0`, then the values of `a_1+b_1` is
A. 2
B. 4
C. zero
D. none of these

Answer 1

Correct Answer - C
The equation of the hyperbola is
`(x^(2))/(9)-(y^(2))/(16)=1`
The equation of the tangent is
`y=mx+sqrt(9x^(2)-16)`
`"or sqrt(9m^(2)-16)=2sqrt5`
`"or "m= pm2`
or a + b = sum of roots = 0