make a careful drawings of the following pairs of parabolas and determine the coordinates of the point of intersection of each pair . (a) 4y^2=3x , 2x^2=9y

Answer 1

4y^2 = 3x is a rightward opening parabola

vertex at the origin

2x^2 = 9y is an upward opening parabola, vertex at the origin

one intersection is the origin (0,0) a 2nd intersection is in the 1st quadrant. x=(4/3)y^2 from the 1st equation. plug it into the 2nd equation.

2((4y^2)/3)^2 = 9y

2(16y^4/9) = 9y

16y^4 = 81y/2 y=0 is one solution, (x,y) =(0,0)

y^3 = 81/32

y = the cube root of 81/32

=cube root of 2.53125

= (3/2)(cube root of 3/4)= about 1.363

x= (4/3)y^2 = (4/3)(1.363)^2 = about 2.477

(x,y) = (2.477, 1.363) is the other intersection point, approximately.