Question 537430
{{{x2+y2+6x-8y=11}}} looks like a circle to me because it has a term in {{{x^2}}}
and a term in {{{y^2}}}, and both have the same coefficient
Adding {{{9+16=25}}}to both sides you get
{{{(x2+6x+9)+(y2-8y+16)=11+25}}} --> {{{(x+3)^2+(y-4)^2=6^2}}}
That is the equation of a circle centered at (-3, 4), with radius 6.
{{{y^2/4-x^2/25=1}}} looks like a hyperbola.
It is centered on the origin and symmetrical with respect to both axes, but you can see that no point with {{{y=0}}} could be on the graph. This curve hates the x-axis; it won't touch it.
The closer it will get to the x-axis is {{{y^2/4=1}}} <-->{{{y^2=4}}} when {{{x=0}}}, so vertices are (0,2) and (0,-2).
The lines {{{y=(5/2)x}}} and {{{y=-(5/2)x}}} are asymptotes.
{{{4x2+y2=16}}} is the equation of an ellipse centered at the origin. The ends of its axes are easy to find, by making {{{x=0}}} or {{{y=0}}}
I do not know what you meant by
(x-1,782,000,000)2/3.42(10)23 + (y-356,400,000)2/1.368(10)22
Perhaps it was
{{{(x-1782000000)^2/(3.42*10^23) + (y-356400000)^2/(1.368*10^22)}}}
but I would expect that to be equal to 1 and be followed by a question about the eccentricity of the orbit of some object that travels along an elliptical path described by that equation.