Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1. f(x) 4 O (x) = -x O (x) = -4x² O f(x) = 4x2

Q: Find the equation of the parabola and put it in the form f(x)= ax^2 +bx+c  Given:  Vertex: (2/3 ,…

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Q: Determine the value of p (where Ip| corresponds to the distance from the vertex to the focus) of the…

A: Given: Vertex of parabola is 3, -6and y-intercepts are 0, -10 and 0, -2. To determine: Value of p.

Q: 8. Find the equation of the parabola ax? + by? + cxy + dx + ey nat passes through the points (3, 1),…

A: A parabola is given by, ax2+by2+cxy+dx+ey+f=0. Also the parabola passes through the points 3,1 and…

Q: Find the coordinates of the vertex of the parabola y = x^2 - 4x + 1 using derivatives O (2, -3) O…

A: To find the vertex of the parabola by using derivatives

Q: 14. Find the maximum and minimum values of the function f(x,y) y? = xy on the ellipse given by the…

A: Given f(x,y)=xy subject to    g(x,y)=x2+y24-1=0 We have to find the maximum and minimum values of…

Q: 11. Find an equation for a hyperbola with asymptotes y=±x and passes through (1, 2).

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Q: 5. Find the maximum and minimum values f(x, y) = xy can take on the ellipse 4x²+y? = 16.

A: The given function f(x,y)=xy to the ellipse 4x2+y2=16

Q: Find the standard equation of the parabola with x intercepts at x = 2 and x -3, and a y-intercept at…

A: Solution is given below

Q: Derive the equation of the parabola with a focus at (-7, 5) and a directrix of y = -11. O (x)= (X +…

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Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

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Q: Find the equation of parabola “y = ax2 + bx + c” passing through points (1, -6), (2, -3), (-1, 0)

A: Consider the given points and the equation of the parabola. Obtain the system of equations with a, b…

Q: Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8. 1 O f(x) -(x –…

A: Given query is to find the equation of parabola.

Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

A: The standard equation of the parabola is x=14f−hy−k2+h where, h,k is the vertex and f,k is the…

Q: The orthogonal trajectory of y=cex is a parabola of the form y2=ax+b. Find the values of a and b so…

A: See the details solution in below

Q: What is the equation of a parabola in standard form with vertex V(3, – 3) and focus F(3, 2)? A (x-…

A: NOTE: Refresh your page if you can't see any equations. . the vertex is at  and the focus is at

Q: Select a possible equation for a parabola with a vertex of (-1,3). Oy = (z + 1) (x – 3) | Oy = (z -…

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Q: Find the equation of the tangent to the hyperbola x2 - 4y2 = 9 at (5, 2).

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Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: The standard equation of the parabola is given as y2=4ax . This parabola has symmetry about the…

Q: Find an equation for the parabola with vertex V(0, 0) and Focus F(0, 2), and sketch its graph.

A: We have given vertex V0,0 and focus F0,2. Given the vertex of the parabola is V0,0 and focus is at…

Q: What is the equation of a parabola that intersects the x-axis at points (-1, 0) and (3, 0)?   A. y…

A: Given that: A parabola intersects x-axis at (-1, 0) and (3, 0)

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1. 1 O f(x) = -- 2…

A: We can derive the equation of parabola as below.

Q: 3. Find the equation of the parabola with focus at F(3,2) and with the line x = -4 as directrix.

A: Topic- equation of parabola from focus ans directrix.

Q: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given by the…

A: We have the given function is f(x,y)=xy    ..... (1)   The equation of ellipse  x2+y24=1 Let…

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

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Q: Find the equation of the tangent to the hyperbola x² – 3y² = 1 at the point S(2,-1). A) 2x + 3y – 1…

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Q: 16. What is the equation, in standard form, of a parabola that models the values in the table? -1…

A: Topic = Quadratic equation Standard form of parabola  equation is  y=ax2+bx+c

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: Given thatthe vertex of the parabola at the origin and focus is(0, -1/2)

Q: Sketch the parabola y = x² + 2x +1. Use arrows to indicate the maximum and minimum values of y over…

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Q: 5. Find the equation of the hyperbola whose asymptotes are the straight lines x = 0 and y = 0 and…

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Q: The function h(x) is the shape of a parabola and has a focus of (0,10) and a directrix through the…

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Q: 5. Find the equation of the following parabola in standard form: f(x) =

A: Given: From the given graph of the parabola, it intersects the x-axis at x=1 & x=3, so it has…

Q: find the general equation of the parabola with horizontal axis which crosses the x-axis at x=2 and…

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Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: Given query is to find the equation of the paraola.

Q: 13. Find the point on the parabola y* = 2x that is nearest the point (1, 4). %3D

A: As per our guidelines we can solve only one question or three sub-parts. To ask more please…

Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

A: Given

Q: - Find a parabola with equation y = ax? + bx +c that has slope 4 at x = 1, slope –8 at x = -1, and…

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Q: 1. Determine the equation of the parabola whose vertex is at the point (-1, –1) and whose directrix…

A: We have to determine the equation of the parabola whose vertex is at the point (-1,-1) and whose…

Q: The asymptote of the hyperbola given by x²/9- y²/4 = 1 has the equation?

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Q: Find the equations of asymptote lines of the hyperbola y-x2+ 14 x-8y 37 Select one: O None Oy =…

A: Given, y2-x2+14x-8y=37

Q: 9.  Find the shorted distance from point A(2, 1/2) to a point on the parabola y = x2. And find the…

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Q: The parabola y + 2y + 8x –7=0 has vertex at O (-1, –1) o (-1,1) о (1,-1) о (1,1)

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Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

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Q: Find the equations of asymptote lines of the hyperbola y-x2+14 x - 8 y = 37 Select one: O None…

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Q: 1. Find the point on the parabola y = 3 – x² that is closest to the point (6, 0).

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Q: 12. Determine the equation of the directrix for the parabola 20x=y2–10y+30 а. X-20 b. y=-20 с. X3-20…

A: Question : Determine the equation of the directrix for the parabola 20x = y^2 - 10y +30.

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

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Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

A: Finding the equation of parabola

Q: 2. Find the equation of the hyperbola whose asymptotes are perpendicular to the lines 5x – 4y +9 = 0…

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Q: Determine the coefficients a, b, and c of the parabola y = ax² + bx +c that passes through the point…

A: Solution is here