Recent content by math12345

Please help with this! I cannot seem to figure it out. A parabola has a focus (1,1) and a vertex (4,5). Find the equation of the directrix, the endpoints of the latus rectum, and the equation in standard form. I have plotted the points but I have no idea how to get the equation because...

A sphere has two parallel tangent planes with equations x+2y-2z=37 and x+2y-2z=-11. One of the points of tangency is (-7,5,7). Find the center and radius of the sphere. I'm not really sure how to do this. I know that the point (-7,5,7) lies on the x+2y-2z=-11 plane. The distance from...

Homework Statement The lines r=(2+2t)i+(3-3t)j+(4-2t)k and v=(4+2s)i+(1-6s)j+(5-3s)k are skew. Find the perpendicular distance between them at the point(s) where they cross over each other. Homework Equations The Attempt at a Solution Does this seem right...

okay, so does this seem right? Direction vectors: The first is the direction vector of the line = (5, -1, -4) , the second is the normal vector of the first plane = (5, -3, 7) And (- 1, 5, 7) is a point of the second plane (and of the first plane) So the equation of the second perpendicular...

The line of intersection of two perpendicular planes is r=(-1+5t)i +(5-t)j +(7-4t)k. One plane is 5x-3y+7z=29. Find the rectangular equation of the other plane. The Attempt at a Solution I think I need to find three points in the desired plane. (one point being (-1,5,7)?)