- #1
Dirac
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vertex (-2, 3), focus (0,3)
Find the equation of the parabola.
Dirac.
Find the equation of the parabola.
Dirac.
What have you tried so far?Dirac said:vertex (-2, 3), focus (0,3)
Find the equation of the parabola.
Dirac.
lurflurf said:What have you tried so far?
Find the directix. then recall
A parabola is the set of point equidistant from the focus and directix.
a will be the distance between the focus and vertex.Dirac said:So far I have got to this
((y-3)^2)=4a(x+2)
What now
Dirac.
lurflurf said:a will be the distance between the focus and vertex.
Why is this?
you started out withDirac said:How does one find the vertex
lurflurf said:you started out with
vertex (-2, 3), focus (0,3)
The points of a parabola are equidistant from it directrix and focus.
The vertex is the point closest to them. that is
distance(vertex,focus)<=distance(point on parabola,focus)
with equality only when the point is the vertex.
I already said you a is the distance betweenDirac said:Could you just post the answer, or would it get up your backside to post something useful in your life
Dirac.
Dirac said:Could you just post the answer, or would it get up your backside to post something useful in your life
Dirac.
A directrix and focus are two important elements in conic sections, such as circles, ellipses, parabolas, and hyperbolas. They are used to define the shape and position of these curves in a coordinate plane.
In conic sections, the directrix is a fixed line that is perpendicular to the axis of symmetry of the curve. The focus is a fixed point on the axis of symmetry. The distance from the focus to any point on the curve is equal to the distance from that point to the directrix. This relationship helps determine the shape of the conic section.
In a parabola, the directrix is a line that is parallel to the axis of symmetry and is located at a distance from the vertex equal to the distance from the vertex to the focus. The focus is the fixed point on the axis of symmetry that gives the parabola its shape. The directrix and focus are used in the standard equation of a parabola: y = (1/4p)(x-h)^2 + k, where p is the distance from the focus to the vertex.
The eccentricity of an ellipse is a measure of how "stretched out" or "squished" the ellipse is. It is determined by the distance between the center of the ellipse and the two foci, divided by the length of the major axis. The closer together the foci are, the higher the eccentricity. The directrix and focus play a key role in determining the eccentricity of an ellipse.
Yes, the directrix and focus can be used to find the equation of a hyperbola. In a hyperbola, the distance from any point on the curve to the focus is always greater than the distance from that point to the directrix. This relationship helps determine the shape and position of the hyperbola in a coordinate plane. The standard equation of a hyperbola is (x-h)^2/a^2 - (y-k)^2/b^2 = 1, where a is the distance from the center to a vertex, and b is the distance from the center to a co-vertex, both measured along the transverse axis.