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?
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?