Given that 16p2 + 49q2 - 4r2 - 56pq = 0. Which one of the following is a point on a pair of straight lines (px + qy + r) (px + qy - r) = 0?

If 3x + y - 5 = 0 is the equation of a chord of the circle x2 + y2 - 25 = 0, then what are the coordinates of the mid-point of the chord ?

Consider the following in respect of the equation $\frac{x^2}{24-k}+\frac{y^2}{k-16}=2$.

1. The equation represents an ellipse if k = 19.

2. The equation represents a hyperbola if k = 12.

3. The equation represents a circle if k = 20.

How many of the statements given above are correct?

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?