Consider the following statements in respect of hyperbola $\frac{x^2}{\cos ^2 \theta}-\frac{y^2}{\sin ^2 \theta}=1$ :

1. The two foci are independent of θ.

2. The eccentricity is sec θ.

3. The distance between the two foci is 2 units.

How many of the statements given above are correct?

Consider the following in respect of the circle 4x2 + 4y2 - 4ax - 4ay + a2 = 0:

1. The circle touches both the axes. 

2. The diameter of the circle is 2a.

3. The centre of the circle lies on the line x + y = a.

How many of the statements given above are correct?

For what values of k is the line (k - 3)x - (5 - k2) y + k2 - 7k + 6 = 0 parallel to the line x + y = 1?

The line x + y = 4 cuts the line joining P(-1, 1) and Q(5, 7) at R. What is PR ∶ RQ equal to ?