Visualizing Conics from Right Circular Cone

Q. The locus of the point $x=t+\frac{1}{t}$ and $y=t-\frac{1}{t}$ is

1. a straight line
2. a circle
3. a parabola
4. a hyperbola

Q. How to expand scalar triple product and vector triple product?

Q. The equation $\lambda x^2+4xy+y^2+\lambda x+3y+2=0$ represents

1. a parabola if $\lambda =4$
2. an ellipse if $\lambda >4$
3. a hyperbola if $\lambda <4$
4. a pair of straight lines if $\lambda =2$

Q. what is cartesian product and its application

Q. 39. How to find the cartesian product