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Math Help - Intersection of a sphere with xz plane

  1. #1
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    Intersection of a sphere with xz plane

    Find an equation of the sphere with center (1,-4,3) and
    radius 5. What is the intersection of this sphere with the xz-plane?

    I know that the equation would be:
    (x-1)^2 + (y+4)^2 + (z-3)^2 = 25

    and the intersection would be
    (x-1)^2 + (z-3)^2 = ?
    but how do you determine the radius of the intersecting circle?

    Any help is greatly appreciated
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  2. #2
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    For all points on the xz plane, y is zero. Since these points must also be on the sphere, you just need to set y to 0 in your equation for the sphere and that will give you the equation of the circle of intersection.
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