What is the (unsigned) distance between the vertex and the focus of the parabola given by (x + 4)² = 19(y + 5) ?

Q: Find the standard equation of the hyperbola. Two corners of auxiliary rectangle at (−4 ,−7) and (0…

A: Given: The two corners of the auxiliary rectangle of a hyperbola are at -4,-7 and 0,0 and transverse…

Q: Sketch the graph of the hyperbola 4x2 − y2 = 16.

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

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Q: What is the equation of the parabola with vertex at (0, 0) and directrix y = -8 in standard form?…

A: Given that, vertex of parabola is (h, k) = (0, 0) diretrix of parabola is, y = -8 We have to find…

Q: find the coordinates of the vertex and the focus for the parabola given by x2+6x+24y-111=0

A: SOLUTION-

Q: How can we find the slope of the parabola y?

A: You can’t find the slope of the parabola y , because a parabola is not a line. You can find the…

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

A: equation of parabola:-

Q: What is the measure of the focal width of the parabola y+2y+4x-3=0 ?

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Q: Find the equation of the parabola with vertex (2, 4) and directrix x = –3

A: Given: Vertex (2,4)

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

A: Given:Vertex=0,0Directrix y=-3Equation of parabola:x-h2=4py-k

Q: Determine the DE for: Parabolas with axis to the x- axis and with distance from focus to  vertex…

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Q: Find the equation for the parabola that has its vertex at the origin and the focal point is 278…

A: Consider the equation of parabola vertex at origin and focus to the right of directrix. y2=4ax…

Q: Find the vertex of the given parabola. Give all values correct to 3 decimal places. y = 7x2 - 8x +…

A: A detailed solution is given below

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…

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

Q: What is the equation of the directrix of the parabola having a vertex at (6,0), passing through…

A: Given:- What is the equation of the directrix of the parabola having a vertex at (6,0), passing…

Q: Find the equation for the parabola that has its vertex at the 1 origin and has directrix at y 41…

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Q: Find b and c so that the parabola with equation y = 4x2 - bx - c has a vertex at (2 , 4)?

A: Using the vertex formula we find the x value of the vertex[formula: x value of vertex of Ax^2+Bx+C=0…

Q: The parabola y2 =-14x has it's focus at the point (b,0) where b is?

A: The standard equation of parabola for this condition is y2=-4ax here  Focus (-a, 0)   Now, we have…

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: What is the directrix, focus, and the vertex of the parabola if Vertex V (3, −2) and axis parallel…

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Q: Explain how to use y2 = 8x to find the parabola’s focus and directrix.

A: Given: y2=8x   To find: The parabola’s focus and directrix

Q: A parabola has an equation of y² = 4x. Find the nearest distance from the point (-3, 6) to the %3D…

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Q: what is the equation of a parabola with a vertex at (4, 8) and a directrix at y=5

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Q: Find the points of intersection between the parabolas y = 6 - x 2 and y = x 2 - 2. %3D

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Q: What are the slopes of the asymptotes for the hyperbola whose equation is 4x2-9y? = 36? %3D

A: Here, the given equation of the hyperbola is: 4x2-9y2=36 In standard from it can be written as:…

Q: Find an equation of the parabola that satisfies the conditions. a) Focus (0, -) and directrix, y =…

A: Given  Focus (0 , -1/2)  Directrix ,y = 1/2   Equation of parabola with focus at (x0 , y0) and…

Q: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

A: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

Q: What is the equation of the parabola with vertex at (0,0) and focus (0, –4) in standard form?…

A: see below the calculation

Q: The distance between the vertex and the focus of a parabola is called the __________ length and is…

A: First of all, consider the definition of the vertex and the focus of a parabola.The vertex of…

Q: What are the coordinates of the end points of the latus rectum of the parabola with equation a - 2z…

A: What are the coordinates of the end points of the latus rectum of the parabola with equation…

Q: Determine the points of intersection of the parabola y=2x^2 +12x +10 and the line y=4x+2

A: I am attaching image so that you understand each and every step.

Q: What is the length of the conjugate axis of the hyperbola (x^(2))/(16)-(y^(2))/(4)=1?

A: General form of hyperbola   x2a2-y2b2=1  Therefore the length of the Conjugate axis =2b…

Q: What is the standard form of the equation of the parabola with the focus (-3, 6) and the directrix y…

A: GIVEN: focus (-3, 6) Directrix y = -2

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

A:

Q: Find the points of intersection of the parabola with equation 2x + y² + 4y – 2 = 0 and the line…

A: Here we find the intersecting point of parabola and the line.

Q: [1] What is the c value of a parabola with a Vertex of (4,2) and a Focus of (4,4)?

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: What is the equation of the parabola with a vertex at (4.8) and a directrix at y = 53

A: This is a simple question based on conic section (Topic is parabola) before attempting this question…

Q: How is the distance between vertices for hyperbola equal to 2a?

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Q: Find the DE of parabolas with vertex and focus on the x-axis.

A: We know that equation of parabola when vertex and focus on the x-axis is, y2=4ax-h  where a and h…

Q: Obtain the X-value of vertex for the parabola defined by y = x2 +8x - 5

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Q: 19. What is the equation of the horizontal asymptote for this hyperbola ? y = (6x + 8) / (3x - 2) *

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Q: Find the equation of the parabola that is symmetric about y axis with vertex at the origin and…

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Q: How is the axis of symmetry related to the vertex, focus, and directrix of a parabola?

A: See the attachment below

Q: Find the equation for the hyperbola that asymptottes (y - 3) = +- 1/square root of 2 * (x+3) and…

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Q: Find the shortest distance of the point (10,4) to the parabola y=x2

A: Consider a  point on parabola  y=x2. Distance of this point with (10,4) s2=(x-10)2+(y-4)2…

Q: What is the Axis of Symmetry of the parabola represented by y = - = -x² – 3x + 7? O x = 3 O x = -3 O…

A: The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent…

Q: Find the shortest distance of the point (6,3) to the parabola y=x2

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Q: Find the standard equation of the parabola which satisfies the given conditions. Vertex (−8,3),…

A: To find the standard equation of parabola