Thread: Conics Review

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.


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


3)Find an equation of the ellipse with vertices's (0,-1) and (12,-1) and minor axis of length 6.


4)Find an equation of the hyperbola with center (2,3), a focus at (2,5), and a focal chord at length 6.

Originally Posted by todd85

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.


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


3)Find an equation of the ellipse with vertices's (0,-1) and (12,-1) and minor axis of length 6.


4)Find an equation of the hyperbola with center (2,3), a focus at (2,5), and a focal chord at length 6.

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.

Using x=a(y - k) + h, and x=2y^2, we have a = 2.

Vertex (-3, 7) and a=2 yields x = 2(y + 7)^2 - 3

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

Center(h, k) = (1, 4) and tangent to y-axis means the radius 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

3)Find an equation of the ellipse with vertices's (0,-1) and (12,-1) and minor axis of length 6.