1)Find the equation of the parabola that opens to the right, has a vertex of(-3,7), and is congruent to the parabola x=2y^2.

Usingx=a(y - k) + h, andx=2y^2, we havea = 2.

Vertex (-3, 7)anda=2yieldsx = 2(y + 7)^2 - 3

2)Find the equation of the circle withcenter (1,4)and is tangent to the y-axis.

Center(h, k) = (1, 4)and tangent to y-axis means theradius is 1(the center is 1 unit from the y axis).

Therefore, using(x - h)^2 + (y - k)^2 = r^2, we have:(x - 1)^2 + (y - 4)^2 = 1