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Math Help - Conics Review

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    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.
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    Quote Originally Posted by todd85 View Post
    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
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    3)Find an equation of the ellipse with vertices's (0,-1) and (12,-1) and minor axis of length 6.

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