A quadratic function with the 
rule is given.
Draw a graph of the 
function in the coordinate system. Prove that the tangents to the graph of the function at the intersection with the 
axis are perpendicular to each other.
The curve with equation 
is an ellipse. Write its equation in standard form 
. Write down its vertices and foci. Calculate the volume of the spindle obtained by rotating the ellipse 
around the 
axis.
The curve with equation 
is a hyperbola. Write its equation in standard form 
and calculate the equations of their asymptotes.
