If the intersection of the line y = x + K and the line y = 2x + 3K is inside the square of the circle (x-1) + the square of y = 1, then the value range of K?

If the intersection of the line y = x + K and the line y = 2x + 3K is inside the square of the circle (x-1) + the square of y = 1, then the value range of K?

y=x+k
y=2x+3k
The solution of simultaneous equations is x = - 2K, y = - K
The intersection coordinates are (- 2K, - K)
The intersection point is inside the circle (x-1) square + y square = 1
(-2k-1)²+(-k)²

Let proposition p: equation x ^ 2 / A + 6 + y ^ 2 / A-7 = 1 denote hyperbola, and proposition q: circle x ^ 2 + (Y-1) ^ 2 = 9 intersects circle (x-a) ^ 2 + (y + 1) ^ 2 = 16
If "P ∧ Q" holds, find the range of real number a

Proposition p: equation x ^ 2 / A + 6 + y ^ 2 / A-7 = 1 represents hyperbola, then (a + 6) (A-7)