Question 91185
The given 3 equations are:  


1) {{{ x^2/9 + y^2/16 = 1 }}} 


This is an equation in the form of {{{ ((x^2/a^2) + (y^2/b^2)) = 1 }}} 


On comparing, we find that the given equation represents an ellipse. 


Hence, the graph looks in this way. 


{{{ graph( 300, 300, -15, 15, -15, 15, 4*(sqrt(1 - x^2/9)),(-4*(sqrt(1 - x^2/9))) ) }}} 


The second equation is: {{{ 4x^2 - 9y^2 = 36 }}}


Comparing this equation with the standard equation {{{ ((x^2/a^2) - (y^2/b^2)) = 1 }}}  we find that the given equation represents a hyperbola.



Hence, the graph looks in this way. 


{{{ graph( 300, 300, -15, 15, -15, 15,(sqrt((x^2 - 36))/3), (-(sqrt((x^2 - 36))/3)) ) }}} 



The third equation is:  


{{{x = (y+1)^2 + 2 }}} 



This can be written as:  


{{{y = (1 +- sqrt(x - 2))}}} 


Hence, the graph looks like this. 


{{{ graph( 300, 200, -6, 5, -10, 10, 1 + sqrt(x - 2), 1 - sqrt(x - 2)) }}}