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

If the values of m for which the line y=mx+2sqrt(5) touches the hyperbola 16x^(2)-9y^(2)=144 are the roots of the equation x^(2)-(a+b)x-4=0 , then the value of a+b is

If the values of m for which the line y= mx +2sqrt5 touches the hyperbola 16x^2 — 9y^2 =144 are the roots of the equation x^2 -(a +b)x-4 = 0 , then the value of a+b is

If values of m for which the line y= mx +2 sqrt5 touches the hyperbola 16x^(2) -9y^(2) =144 are roots of the equation x^(2) -(a+b)x-4 =0 then value of (a+b) is equal to

Values of m, for which the line y=mx+2sqrt5 is a tangent to the hyperbola 16x^(2)-9y^(2)=144 , are the roots of the equation x^(2)-(a+b)x-4=0 , then the value of (a+b) is equal to

Values of m, for which the line y=mx+2sqrt5 is a tangent to the hyperbola 16x^(2)-9y^(2)=144 , are the roots of the equation x^(2)-(a+b)x-4=0 , then the value of (a+b) is equal to

The values of m for which the lines y = mx + 2 sqrt5 touches the hyperbola 16 x^(2) - 9y^(2) = 144 are the roots of x^(2) - (a+b) x-4 = 0 then the value of (a+b) is

Show that the line y =x + sqrt7 touches the hyperbola 9x ^(2) - 16 y ^(2) = 144.

The values of lamda for which the line y=x+ lamda touches the ellipse 9x^(2)+16y^(2)=144 , are