Answer to this question
2 answers:
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Answer:
If Discriminant,
Then it has Two Real Solutions.
Step-by-step explanation:
To Find:
If discriminant (b^2 -4ac>0) how many real solutions
Solution:
Consider a Quadratic Equation in General Form as
then,
is called as Discriminant.
So,
If Discriminant,
Then it has Two Real Solutions.
If Discriminant,
Then it has Two Imaginary Solutions.
If Discriminant,
Then it has Two Equal and Real Solutions.
The cone equation gives
which means that the intersection of the cone and sphere occurs at
i.e. along the vertical cylinder of radius
when 
.
We can parameterize the spherical cap in spherical coordinates by
where
and 
, which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is . So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is
Now the surface area of the cap is given by the surface integral,
which means that the intersection of the cone and sphere occurs at
i.e. along the vertical cylinder of radius
We can parameterize the spherical cap in spherical coordinates by
where
Now the surface area of the cap is given by the surface integral,