IV. Transform the given general form of the equation of a parabola into its standard form 1. y = 4 (x2 – 2x + 5) 2. 3x2- 12x - 84y + 124 = 0 3. 4y2+ 12y – 32x + 41 = 0

Q: Find the equation of the parabola with vertex at the origin and satisfies the condition: Focus…

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Q: A. Reduce each of the following equations of hyperbolas in standard form. 1.) 4x² – y? + 2y - 5 = 0…

A: We have to obtain the standard form of the given equations.

Q: What is the standard form of the parabola, y + 2x + 10y + 9 = 0, given in conic form?

A: Do some rearrangement in the equation of given conic to convert it in standard form of equation

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

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Q: Which of the following equations represents the parabola with vertex at (3, 2) and directrix y = 4?…

A: To find out the equation of the parabola.

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: transform into standard form of hyperbola x^2-y^2+6x-4y-4=0

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Q: In the xy-plane, if the parabola with equation y = ax² + bx + c, where a, b, and c are constants,…

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Q: 3) Fit a parabola to the data. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y 3.1950 3.2299 3.2532 3.2611…

A: the equation of the parabola is given by y=ax2+bx+c we have to use the calculator to find the…

Q: 3- The parabola y= ax'+bx+e, mean that the equation y ax' is . .........

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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: A. Reduce eachof the following equations of hyperbolas in standard form. 1.) 4x² – y² +2y - 5=0 2.)…

A: To write the given equation of a hyperbola in its standard form.

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: Find three points on the parabola. x^2−8x−8y−8=0

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

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Q: c. Convert the equation of a parabola from general to standard form x? + 4x + 8y + +36 = 0 d.…

A: We know that the general equations of parabola is y2 = 4ax and the standard equations of parabola is…

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: Convert the following equation for a hyperbola into standard form. -x2 + 4x + 25y² + 150y + 196 = 0…

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

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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: 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: find the points on the parabola y=x^2 closest to the point (0,1)

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Q: Which of the following equations of parabolas has its vertex at (1, 2)? O y= 12 + 2x + 3 O y= r² +…

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

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Q: Find the equation of the line tangent to the hyperbola x2 −y2 =16 at (5,3).   Give your answer in…

A: The line is tangent to the given hyperbola at (5,3).Tangent line is a straight line.Therefore, the…

Q: 10. Draw the hyperbola with the equation: 3x? – 2y² + 6x – 8y = 6.

A: The given equation of hyperbola is: 3x2-2y2+6x-8y=6 Converting it into the normal form of hyperbolic…

Q: 1. For the parabola equation: (y-2) = -3(x+4)^2 + 7, in which direction does the parabola open? *

A: We have to find the direction in which the given parabola opens.

Q: 22. Which of the following is the equation for a parabola with a vertex of (3, 1) and a focus of (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: 9. Find an equation of the hyperbola whose transverse axis is horizontal, with center at (2, –2) and…

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Q: The equation of the line touching both the parabolas y = 4x and x' =-32y is x-2y+1 = 0, then a is

A: Introduction :

Q: 1. If y varies indirectly as a, and y = 3 when a = 4, what is y when a = 6? %3D y = 2 y = 1 y = 4 y…

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Q: Find an equation of the parabola deseribed. Focus at (5, 0); vertex at (0, 0) O y = 20x2 O x = 20y O…

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Q: The graph of y = (2x – 8) (x - 2) is a parabola in the Ty plane. In which of the following…

A: Given  y = (2x-8)(x-2)

Q: 4. Determine whether a hyperbola exists if it has an equation of x2 - y2 + 6x +36y = 18.

A: we have to determine whether a hyperbola exists if it has an equation of  x2-y2+6x+36y=18

Q: 1. Which is the standard form of the parabola y =-}(x+1)² + 5 O y=D -a2 - 긍 + 5.5 O y = -a² + x+ 5.5…

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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: Find the equations of the normal and the tangent to the hyperbola xy + 2x - 5y-2= 0 at the point (3,…

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Q: (a) Find and identify the traces of the quadratic surface x2 +y2 -z2 =1 and explain why the graph…

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Q: 3- The parabola y= ax'+bx+c, mean that the cquation y = ax is .........

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: Which of the following is the standard form of the given parabola? 2y² – x – 8y - 8 = 0 %3D (y + 2)2…

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Q: D. Directions. Convert the following equations of parabola into then standard form. 1. y2 - 4x- 6y +…

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Q: Write each standard equation of Hyperbola in a General form (Ax² + By² + Cx + Dy + E = 0, where AB <…

A: a. Consider the given equation of hyperbola, x+625-y-121=1 the general form of the hyperbola is…

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: 6. After a reflection in the x-axis, the parabola y =x -4 would have the equation (1) y=x²+4 (3)…

A: Reflection in x axis

Q: 3. Write the equation into the standard form of the equation of the hyperbola: x² – 4xy + y² + 8x +…

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Q: Find the parabola with equation y = ax? + bx whose tangent line at (2, 8), is y = -2x + 12.

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