Question 750757
How do I write equation for each conic section:
Circle with center at (0 ,-3) and the radius of 5
Standard form of equation for a circle: {{{(x-h)^2+(y-k)^2=r^2}}}, (h,k)=center, r=radius
For given circle:
center: (0,-3)
radius=5
{{{x^2+(y+3)^2=25}}}
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Parabola with Vertex at (-3,5) and focus at (-1,5)
Parabola opens rightward:
axis of symmetry: y=5
Its basic equation: {{{(y-k)^2=4p(x-h)^2}}}, (h,k)=(x,y) coordinates of vertex
For given parabola:
p=2(distance from vertex to focus on the axis of symmetry
4p=8
Equation:{{{(y-5)^2=8(x+3)}}}
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Ellipse with the vertices at (2,5) (2,-3) and co-vertices at (0,1) (4,1)
Given ellipse has a vertical major axis
Its standard form of equation: {{{(x-h)^2/b^2+(y-k)^2/a^2=1}}}, a>b, (h,k)=(x,y) coordinates of center
For given ellipse:
x-coordinate of center=2
y-coordinate of center=1 (midpoint of vertex)
center: (2,1)
a=4 (distance from center to vertices)
a^2=16
b=2(distance from center to co-vertices)
b^2=4
Equation of given ellipse: {{{(x-2)^2/4+(y-1)^2/16=1}}}