All three of these questions fall into the category of basic equations of the particular conic
In your text or class notes, you should have these equations listed along with their particular attributes.
Here is a webpage that summarizes the topic nicely
https://www.varsitytutors.com/hotmath/hotmath_help/topics/conic-sections-and-standard-forms-of-equations
I will do the last one:
Write the equation for the conic section if the vertices are at (0,+/-6) and the foci are at (0,+/-10) (Hyperbola)
We can see that the vertices and foci lie on the y-axis
so we have the form
x^2/a^2 - y^2/b^2 = -1
in a hyperbola: a^2 + b^2 = c^2
for yours:
6^2 + b^2 = 10^2
b^2 = 64
equation:
x^2 / 36 - y^2 / 64 = -1
Write the equation for the conic section of the cone is centered at (0,0), the major axis is 10 units and the minor axis is 6 units. (Ellipse)
Write the equation for the conic section if the vertex is (-6,4) and the focus is (-6,7) (Parabola)
Write the equation for the conic section if the vertices are at (0,+/-6) and the foci are at (0,+/-10) (Hyperbola)
TYSM FOR ALL OF HELP! but SERIOUS ANSWERS ONLY PLEASE!
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