Determine the general equation of a parabola opening downwards whose vertex is at (3,-4) with a latus rectum length of 4. O y + 16x + 8y - 32 = 0 O y + 4x + 8y + 4 = 0 x² - 6x +4y + 25 = 0 O x² - 6x + 16y + 73 = 0

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: Find the standard form of the equation of the parabola with the given characteristics. Vertex:…

A: General equation of parabola,(x-h)2 = 4p(y-k)where (h,k) is Vertexy = k-p is directrix

Q: Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2…

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Q: There is a parabola which has a minimum where the two lines 3x+6y-1=0 and 2x+ y-2=0 intersect. The…

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Q: Which of the following is the equation of the parabola shown below? 10-y 8+ 6+ (4,2) 2- .0) + -4 -2…

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Q: 8) Find the equation of the parabola in vertex form. (A) y=3(x-2)2+2 (B) y-3(x-2)2-2 (C) y-3(x+2)2+2…

A: Topic - equation of a parabola A parabola is a conic section made by the intersection of a right…

Q: The vertex of a parabola is located at (−5, 6). If the parabola has a y-intercept of (0, 231), which…

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Q: 7. Determine all values of a that will cause the parabola y=ax² +10x+1 to cross the x-axis at two…

A: 7) y=ax2+10x+1 ...................eq (1) For parabola to cross the x- axis put y=0 0=ax2+10x+1…

Q: The equation of the parabola that has a vertical axis of symmetry, touches the x-axis and has its…

A: Given, The parabola has vertical axis of symmetry touches the x axis and has its focus at 1, 7 We…

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: What is the equation in vertex form of a parabola with a vertex of (-3, 4) that passes through the…

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Q: parabola

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Q: The vertex of the parabola f(z) = + 6z + 7 is O (-3,-2) O (-6,-18) O (-6, -2) O (-3,5) O (-9,-2)

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: What is the equation of the parabola containing the points (0, 5), (–1,9), and (2, 3)? O y = r-z+5 O…

A: The standard form of a parabola is y=ax2+bx+c. The required parabola passes through the 3 points are…

Q: Find the standard form of the equation of the parabola with the given characteristics. vertex: (2,4)…

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Q: The equation of the parabola whose vertex is located at (7,6) and its focus is ( 7,-4) Select one:…

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Q: transform into standard form of hyperbola 4y^2-9x+16y+18x-29=0

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Q: Find the equation y=ax^2+bx+c of the parabola that passes through the points (-2, 0), (0, -14), (7,…

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Q: Find the standard form of the equation of the parabola with the given characteristic and vertex at…

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Q: Find the vertex of the parabola. y = 3x² - 1 О (0, (0, –1) O (-1, 3) O (-1, 0) (3, –1) (0, 3)

A: topic - parabola

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: 5. What is the standard for equation of a parabola with its vertex at (0,0) and a directrix of x-3?…

A: Given: A parabola has vertex 0, 0 and directrix x=3      ……1   To find: Equation of parabola

Q: Find the point on the parabola y = (x – 3)² – 5 that is closest to the point (0,0). |

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Q: Consider a parabola that intersects the x-axis at points (-1, 0) and (3, 0).

A: We need to find an equation of parabola that intersects the x-axis at (-1, 0) and (3, 0). Thus,…

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

A: We have Vertex=(0,0)Directrix x=-15

Q: Find the length of the hyperbola. (y-2)2/ 9 - (x+1)2/4 =1

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Q: How to convert 3y^2-x^2-9=0 into standard form? I know it is a hyperbola.

A: Answer and explanation is given below..

Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2 Ans: 2xy" - 4yy"…

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Q: What is the equation of the parabola in general form given its vertex at (-1,-5) and focus at…

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Q: The area bounded by the parabola y2 = 4ax, its axis, and its latus rectum revolves  about the x-

A: The given equation of parabola is y2=4ax. The objective is to calculate the area bounded by the…

Q: Find the equation of a parabola that has a vertex of (-2, -1) and contains the point (0, 3).…

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Q: (3) Find the coordinates of the points of intersection of the parabola y = x2 - ax and the line y =…

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Q: Show that the line b2xx1 - a2yy1 - a2b2 = 0 is tangent to the hyperbola b2x2 - a2y2 - a2b2 = 0 at…

A: Find dy/dx.Then find dy/dx at the point (x1,y1) by plugging x=x1 and y=y1

Q: How do I solve this optimization problem?

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Q: Determine the standard equation of the parabola opening upward, with focus at (0,6) and whose length…

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Q: 2. Which of the equations below also represents the parabola y=-3x² 18x + 16? Oy=3(x+3)² +65…

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Q: The equation of the parabola that has a vertical axis of symmetry, touches the x-axis and has its…

A: The equation of parabola on x-axis of symmetry is y^2 = 4ax.

Q: Find the standard equation of any parabola that has vertex V.

A: Standard equation of a parabola with vertical axis. The graph of the equation y=ax-h2+k for a≠0 is a…

Q: The graph of y^2 = x^3 is called a semicubical parabola. Determine the constant b so that the line y…

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Q: A parabola has the following properties: axis vertical, passes through (-1,0), (5,0) and (1,8). Find…

A: Topic = Parabola

Q: What is the standard equation of the parabola which satisfies the following properties: V(-4,2),…

A: Let's find.

Q: The vertex of the parabola f(x) = a+ 14z + 10 is %3D о (-14, -63) о (-21, -39) о (-14, -39) о (-7,…

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Q: . Find the vertices of the hyperbola. 16x2 - 9y? = 144 %3D (0, O (0, - 3) and (0, 3) O (0, - 4) and…

A: This question is related to hyperbola, We will solve it using given information.

Q: Find the equation of the parabola y = ax^2 + bx +c that passes through the points (-1,-4) (1,4), and…

A: topic  -  parabola

Q: Find the Equation of a Quadratic (Parabola) Given 3 Points y=a^2+bx+c (0,0), (-3,3), (3,3) Also,…

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Q: Find the standard form of the equation of the parabola that has a vertex at (1,-3) and passes…

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Q: Find the equation of the line tangent to (a) The parabola z = 2x² - 3y², y = 1 at the point (-2,1,5)…

A: Given: we have to find equation of tangent lines   equation of tangent line : y-y1=m(x-x1)

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

A: Solution is here