The location of the focus of the parabola x2 – 6x – 12y – 51 = 0  is at a. (2, -3)           b.  (3, -5)                      c. (2, -5)           d.  (3, -2)

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: The focus of the parabola y^2 = 4x is at

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Q: dr if F= and C is a piece of the parabola y=4-x² from the point (–1,3) to the point (2,0).

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Q: Find an equation of the hyperbola that has foci at (-13,0) and (13,0), and asymptotes y=3/2x and…

A: Given:

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: Find the angle at which the parabola y=x2−14 intersects the positive x−axis.

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

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

A: Given: Focus: F0,-34 To Find: Equation of the parabola that has vertex at the origin and satisfies…

Q: Find an equation of the hyperbola that has foci at (0, -15) and (0, 15), and asymptotes y= 3 3 2x…

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Q: Find an equation of the hyperbola that has foci at (0,-13) and (0,13), and asymptotes y=5/12x and…

A: The hyperbola that has foci at (0,-13) and (0,13), and asymptotes y=5/12x and y=-5/12x. To find…

Q: Find an equation of the hyperbola that has foci at (0, -6) and (0, 6), and asymptotes y=x and y=-x.…

A: We will solve the problem

Q: Sketch the graphs of the parabolas (a) x² = 12y (b) y² + 8x = 0 and show the focus and directrix of…

A: If we have parabola in the form of  x2 = 4ay, which is a upward parabola    Then equation of…

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 focus of the parabola y=1/2-x-1/2x^2

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Q: find the equation of the parabola y = ax? + bx + c that passes through the points. (0, 3), (1, 4),…

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Q: The parabola y=x^2+13 has it's focus at the point (b,c) where  b= c=

A: The given equation of the parabola is, y = x2+13. Also the parabola has its focus at (b, c).Consider…

Q: Consider the graph of  y = ax2 + bx + c, where a = -3, b = 2 and c = 1.  Is the parabola concave up…

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Q: A] Find the length of the arc of the semi-cubical parabola y² = x3 (1,1) and (5,5V5). between the…

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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: 5. Identify the focus of the parabola given by y = 8x². O (0,) O (-8,0) O (0,0) O (8)

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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: 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: Show that the number 4p is the width of the parabola x2 = 4py (p>0) at the focus by showing that…

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Q: Show that the graph of an equation of the formAx2 + Cy2 + F = 0 A ≠ 0, C ≠ 0, F ≠ 0where A and C are…

A: Consider the given equation Ax2+Cy2+F=0, A≠0, C≠0, F≠0 A and C are opposite in sign. So,…

Q: How far from the x axis is the focus of the hyperbola (x^2)- (2y^2) + 4x + 4y+ 4 = 0?

A: the given equation of hyperbola is  x2- 2y2+4x+ 4y + 4 =0 it is asked to find how far is focus of…

Q: Find an equation of the parabola in standard form: with focus at F(7,-1) and directrix 6 units from…

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Q: Find an equation of the hyperbola that has foci at (-2, 0) and (2, 0), and asymptotes y = x and…

A: The hyperbola has foci at -2,0 and 2,0 and asymptotes y=x and y=-x

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

A: Solution Given V=(0,0)F=(a,0)=(5,0)To find the equation of the parabolaFormula:y2=4ax

Q: Find an equation of the hyperbola that has foci at (0, -10) and (0, 10), and asymptotes y = 1 x and…

A: To find the equation of hyperbola

Q: Find an equation of the hyperbola that has fodi at (-15,0) and (15, 0), and asymptotes y=x and y =

A: here we have to find the equation of hyperbola that has foci  at (-15,0) and (15,0) asymptotes…

Q: Find the point on the parabola * +y“ that is closest to the point (0, -3). =

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Q: Find an equation of the hyperbola that has foci at (-10,0) and (10,0) , and asymptotes y=3x and…

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Q: Can you assist me in answering this? (Not graded - solely for acquisitional purposes)

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Q: Find the directrix for the parabola. y = 20 (x+ 2)² - 3 1- x= -1 O y = -1 O y = -8 y 3= O x = -8

A: We will find out the required equation of directrix.

Q: Find the point on the parabola y 2 =2x that is closest to the  point ( 1, 4)

A: Given: y2=2x let's point on parabola is t22,t now, if point1,4 is closest to t22,t2 then product of…

Q: Find the vertex, focus and endpoints of the latus rectum of the parabola  4y^2 - x + 2 y = 0

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Q: Which of the following represents a parabola with vertex at (4, -2) and focus at (4, 4)? O A. (x -…

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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: Fid the equation of the tanget to the parabola  x2 - 22x + 24y +169 = 0 at  the point whose focus…

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

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Q: Find the point(s) of intersection of the parabolas y =x2 andy = -x2+ 8x.

A: Definition used-      Point of intersection-           For finding the point of intersection of…

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: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

Q: Write an equation for the hyperbola that has foci at (0, v65) and (0, - v65), and asymptotes y =…

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Q: 4) Find the equation of a parabola which has the focus at (2,9) and the directrix at x=10.

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Q: Find an equation of the hyperbola that has foci at (-10, 0) and (10, 0), and asymptotes y = 7x and…

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

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Q: Find the vertex Focus and divertrix to given the parabola x2 +6x+8y+25-0

A: The given equation is: x2+6x+8y+25=0 That can be written as…