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How do you write an equation of a parabola with vertex at the origin and the given focus 60?
To write the equation of a parabola with its vertex at the origin (0, 0) and a focus at (0, 60), you first identify the orientation of the parabola. Since the focus is above the vertex, the parabola opens upwards. The standard form of the equation for a parabola that opens upwards is ( y = \frac{1}{4p}x^2 ), where ( p ) is the distance from the vertex to the focus. Here, ( p = 60 ), so the equation becomes ( y = \frac{1}{240}x^2 ).
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Which equation represents a parabola opening to the right with a vertex at the origin and a focus at (40)?
The equation that represents a parabola opening to the right with its vertex at the origin (0,0) and a focus at (4,0) is given by ( y^2 = 4px ), where ( p ) is the distance from the vertex to the focus. Since the focus is located at (4,0), ( p = 4 ). Therefore, the equation of the parabola is ( y^2 = 16x ).
What is the standard equation for vertex at origin opens down 1 and 76 units between the vertex and focus?
Since the vertex is at the origin and the parabola opens downward, the equation of the parabola is x2 = 4py, where p < 0, and the axis of symmetry is the y-axis. So the focus is at y-axis at (0, p) and the directrix equation is y = -p. Now, what do you mean with 1 and 76 units? 1.76 units? If the distance of the vertex and the focus is 1.76 units, then p = -1.76, thus 4p = -7.04, then the equation of the parabola is x2 = -7.04y.
How does an equation for a sideways parabola look like?
An equation for a sideways parabola can be expressed in the form ( y^2 = 4px ) for a parabola that opens to the right, or ( y^2 = -4px ) for one that opens to the left. Here, ( p ) represents the distance from the vertex to the focus. The vertex of the parabola is at the origin (0,0), and the axis of symmetry is horizontal. If the vertex is not at the origin, the equation can be adjusted to ( (y-k)^2 = 4p(x-h) ), where ((h, k)) is the vertex.
What is the equation of the parabola with focuse (07) and the directrix y1?
To find the equation of the parabola with focus at (0, 7) and directrix ( y = 1 ), we first determine the vertex, which is the midpoint between the focus and the directrix. The vertex is at ( (0, 4) ). The distance from the vertex to the focus is 3, so the parabola opens upward. The equation of the parabola can be expressed as ( (x - h)^2 = 4p(y - k) ), where ( (h, k) ) is the vertex and ( p ) is the distance from the vertex to the focus. Thus, the equation is ( x^2 = 12(y - 4) ).
What is the equation of a parabola with Vertex (0 0) and focus (-3 0) a.y2-4x b.y2-12x c.y24x d.y212x?
The equation of a parabola with a vertex at the origin (0, 0) and a focus at (-3, 0) opens to the left. The standard form for such a parabola is ( y^2 = -4px ), where ( p ) is the distance from the vertex to the focus. Here, ( p = 3 ), so the equation becomes ( y^2 = -12x ). Therefore, the correct answer is b) ( y^2 = -12x ).
Which equation represents a parabola opening to the right with a vertex at the origin and a focus at (40)?
The equation that represents a parabola opening to the right with its vertex at the origin (0,0) and a focus at (4,0) is given by ( y^2 = 4px ), where ( p ) is the distance from the vertex to the focus. Since the focus is located at (4,0), ( p = 4 ). Therefore, the equation of the parabola is ( y^2 = 16x ).
What is the equation of a parabola with a vertex at 0 0 and a focus at 0 6?
The standard equation for a Parabola with is vertex at the origin (0,0) is, x2 = 4cy if the parabola opens vertically upwards/downwards, or y2 = 4cx when the parabola opens sideways. As the focus is at (0,6) then the focus is vertically above the vertex and we have an upward opening parabola. Note that c is the distance from the vertex to the focus and in this case has a value of 6 (a positive number). The equation is thus, x2 = 4*6y = 24y
What is the standard equation of a parabola that opens up or down and whose vertex is at the origin?
focus , directrix
What is the standard equation for vertex at origin opens down 1 and 76 units between the vertex and focus?
Since the vertex is at the origin and the parabola opens downward, the equation of the parabola is x2 = 4py, where p < 0, and the axis of symmetry is the y-axis. So the focus is at y-axis at (0, p) and the directrix equation is y = -p. Now, what do you mean with 1 and 76 units? 1.76 units? If the distance of the vertex and the focus is 1.76 units, then p = -1.76, thus 4p = -7.04, then the equation of the parabola is x2 = -7.04y.
How does an equation for a sideways parabola look like?
An equation for a sideways parabola can be expressed in the form ( y^2 = 4px ) for a parabola that opens to the right, or ( y^2 = -4px ) for one that opens to the left. Here, ( p ) represents the distance from the vertex to the focus. The vertex of the parabola is at the origin (0,0), and the axis of symmetry is horizontal. If the vertex is not at the origin, the equation can be adjusted to ( (y-k)^2 = 4p(x-h) ), where ((h, k)) is the vertex.
What is the equation of the parabola with focuse (07) and the directrix y1?
To find the equation of the parabola with focus at (0, 7) and directrix ( y = 1 ), we first determine the vertex, which is the midpoint between the focus and the directrix. The vertex is at ( (0, 4) ). The distance from the vertex to the focus is 3, so the parabola opens upward. The equation of the parabola can be expressed as ( (x - h)^2 = 4p(y - k) ), where ( (h, k) ) is the vertex and ( p ) is the distance from the vertex to the focus. Thus, the equation is ( x^2 = 12(y - 4) ).
What is the equation of a parabola with Vertex (0 0) and focus (-3 0) a.y2-4x b.y2-12x c.y24x d.y212x?
The equation of a parabola with a vertex at the origin (0, 0) and a focus at (-3, 0) opens to the left. The standard form for such a parabola is ( y^2 = -4px ), where ( p ) is the distance from the vertex to the focus. Here, ( p = 3 ), so the equation becomes ( y^2 = -12x ). Therefore, the correct answer is b) ( y^2 = -12x ).
What is the equation of the parabola with focus (1 3) and vertex at (3 3)?
The equation of a parabola can be determined using its focus and vertex. Given the focus at (1, 3) and the vertex at (3, 3), the parabola opens horizontally since the x-coordinate of the focus is less than that of the vertex. The standard form for a horizontally opening parabola is ((y - k)^2 = 4p(x - h)), where (h, k) is the vertex and p is the distance from the vertex to the focus. Here, (p = -2) (the focus is 2 units left of the vertex), so the equation is ((y - 3)^2 = -8(x - 3)).
What is the equation of the parabola when the vertex is (3 2) and the focus is (5 2)?
The equation of a parabola can be derived from its vertex and focus. Given the vertex at (3, 2) and the focus at (5, 2), the parabola opens to the right. The standard form of the equation is ((y - k)^2 = 4p(x - h)), where ((h, k)) is the vertex and (p) is the distance from the vertex to the focus. Here, (h = 3), (k = 2), and (p = 2) (the distance between x-coordinates of the vertex and focus), leading to the equation ((y - 2)^2 = 4(x - 3)).
What is the focus of the parabola y equals 4x2?
The equation ( y = 4x^2 ) represents a parabola that opens upwards. To find the focus, we can rewrite it in the standard form ( y = 4p(x - h)^2 + k ), where ( (h, k) ) is the vertex and ( p ) is the distance from the vertex to the focus. Here, the vertex is at the origin ( (0, 0) ) and ( 4p = 4 ), so ( p = 1 ). Thus, the focus of the parabola is located at the point ( (0, 1) ).
What is the focus of the parabola y 4x2?
The equation of the parabola ( y = 4x^2 ) can be rewritten in the standard form ( y = 4p(x - h)^2 + k ), where ( (h, k) ) is the vertex. Here, it is clear that the vertex is at the origin (0, 0) and ( 4p = 4 ), giving ( p = 1 ). The focus of the parabola is located at ( (h, k + p) ), so the focus is at the point ( (0, 1) ).
What is the point directly above the focus?
The point directly above the focus is the vertex of the parabola. The focus is a specific point on the axis of symmetry of the parabola, and the vertex is the point on the parabola that is closest to the focus.
