I need help with some tricky problem in math...please help!?

I need help with some problems- please help!


1.) The equation x² + y² - z² =1 has:


a.) horizontal slices that are circles and vertical slices consisting of parabolas


b.) horizontal slices that are hyperbolas (with a couple of exceptions) and vertical slices consisting of circles


c.) horizontal slices that are circles and vertical slices that are hyperbolas (with a couple of exceptions)


d.) horizontal slices that are parabolas and vertical slices that are hyperbolas (with a couple of exceptions)





2.) Consider the plane with normal vector %26lt; 2,-1,5%26gt; which passes through the point (1,3,2). Where does this plane intersect the z-axis?


(0,0,2)


(0,0,9/5)


(0,0,11/5)


(0,0,13/5)





I would really appreciate any help! thank you so much!!

I need help with some tricky problem in math...please help!?
for each horiontal slice, z is constant.


x^2+y^2 = 1+z^2 which is a circle


a vertical slice parallel to the x-axis has x as constant.


y^2-z^2 - 1-x^2 is a hyperbola.


a vertical slice parallel to the y-axis has y constant


x^2-z^2 = 1-y^2 is a hyperbola.


c.)





the plane has equation 2x-y+5z = c,


use our point to find c.


-2-3+10=c


c=5


2x-y+5z=5


the z-axis is where x and y are 0,


5z-5, z=1.


(0,0,1)