Question

How do you get an equation of a tangent at a point without an equation

Answer 1

I don't think the question is clear...? What do you mean by "get an equation of a tangent... without an equation"?

Answer 2

we get a picture of an ellipes with a point
and we need to find the tangent line equation

Answer 3

Do we know where it's centered and what its major/minor axes are?

Answer 4

no

Answer 5

This is the graph we got and we need the tangent line of the right point

Answer 6

the curve is an ellipse centered at (2,3) and major axis a=3, minor axis b=2
from this, you can get the equation of the function and then using derivative steps, get the equation of the tangent