Find the equation, in standard form, of the parabola with the specified features. Find the equation of the circle whose center lies in the (common) axis of the parabolas y2 + 4x + 6y = -53 and y2 - 4x + 6y = 3, and which is tangent (touxhes at exactly one point) each of the two parabolas

Q: The x-axis and the y-axis are asymptotes of the equilateral hyperbola whose equation is xy = 9. Find…

A: Given: xy=9 we know that length of transverse axis and conjugate axis is equal for rectangular…

Q: Write an equation for the hyperbola that has foci at (0,1113) and (0,- 113), and asymptotes y = +…

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Q: Classify the graph of the equation 9x2 + 9y2 − 36x + 6y + 34 = 0 as a circle, a parabola, an…

A: Since the coefficients of x2 and y2 are the same and are of the same sign too. So this given…

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

A: Topic = parabola

Q: Find the vertex, focus, and directrix of the parabola x2 − 2x − 4y − 7 = 0 , and sketch its graph.

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Q: Classify the graph of the equation 25x2 − 10x − 200y − 119 = 0 as a circle, a parabola, an ellipse,…

A: On simplification, we get

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: Find the equation of the hyperbola having center at the origin with transverse axis on the x-axis,…

A: Given-  Hyperbola having center at the origin with transverse axis on the x-axis, a=4, and latus…

Q: The equation of a family of parabolas with axis parallel to the y-axis is

A: We will find the equation of family of parabolas with axis parallel to the y-axis .Below find the…

Q: Find an equation of the circle that has a diameter as the distance between the two vertices of the…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: Find the equation of the parabola with vertex at the origin and focus F (0, 5)

A: General equation of parabola with vertex at origin and focus on y axis is x^2= 4ay.

Q: Find the focus and directrix of the parabola with the given equation. 4) 9x2 = -5y

A: Compare standard equation of parabola

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

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Q: Find the vertex of the parabola defined by the following equation: (y – 2)² = –4x – 8 - -

A: Given : y - 22 = -4x - 8

Q: What is the y-intercept of the following parabola?

A: The question is taken from the parabola in which we have to find the y-intercept of the given…

Q: Find the equation of the axis of symmetry of the following parabola algebraically y = -x + 8x

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Q: Find the equation of the directrix of the parabola y=16x.

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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 the general equation of the parabola with vertex at the origin and focus at (-4, 0)

A: The general equation of a parabola with vertex (h,k) is (y-k)2=4a(x-h)

Q: Find the equation of a parabola having directrix y = -5.

A: if given equation of the directrix y= -a then equation of the parabola is  x^2 = 4ay

Q: Find the standard form of the equation of the parabola. Vertex at the origin, focus at (0, 8)

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Q: Find the equation of a parabola with vertex at ( -1, 2) and focus at ( - 1, 3)

A: We have to find the equation of a parabola with vertex at ( -1, 2) focus at ( - 1, 3)   First we…

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

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Q: Find an equation for the indicated half of the parabola.Right half of (x + 1)2 = y - 4

A: (x+1)2=y-4

Q: Sketch the parabola and line on the same graph. y = x + 4 and y = 2x + 2 %D

A: Consider the given parabola y=x2+4 and the line y=2x+2. Use online graphing calculator and sketch…

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

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Q: Given a parabola with vertex at (8,-4) and focus at (-4,-4), determine the equation of the parabola.…

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Q: Find the equation of the parabola in standard form with focus at (7, -6) and vertex 5 units at the…

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Q: Find a Cartesian equation for the curve and identify it as either a hyperbola, circle, limaAson,…

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Q: Write the equation of the parabola with the focus at (−4, 0) and the directrix is x = 4

A: Given that Focus (-4,0) and the directrix is x=4 and we find equations of parabola.   Here i…

Q: The center of a circle is the vertex of the parabola y2 + 24x−12y + 132 = 0. If the circle…

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Q: Find an equation of the hyperbola (in general form) given the following conditions C(2, 5),…

A: Given : For a hyperbola Center C(2,5), Horizontal transverse axis of length 10 Conjugate axis of…

Q: What is the axis of symmetry of the parabola with equation (y - 1) = 4 (x – 1) ?

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Q: Find the equation for the parabola that has its vertex at the origin and has a focus at (18.1, 0).…

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

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Q: What is the equation of the directrix of the parabola X+2x+4y-27=0 2

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Q: Determine the direction in which the parabola opens, and the vertex. y2-10y-x+23=0

A: Add x to both sides. So, this is a parabola of the form y=ax^2+bx+c with a=1=positive number. So…

Q: Find the standards form of the equations of the below parabolas with the given characteristics.

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Q: Find an equation of the parabola that satisfies the given conditions.Vertex at the origin, symmetric…

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Q: Find the vertex, focus, and directrix of the parabola and sketch its graph, for the following…

A: The equation of the parabola is . By simplifying the given equation of parabola it becomes,

Q: Find an equation of the parabola with vertex (5, – 1) and directrix y = -4.

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Q: Find the standard form of the equation of the parabola. Vertex at the origin, focus at (2, 0)

A: General equation of horizontal parabola is given by -y-k2 = 4px-h             ..........(1)where, h,…

Q: Consider the parabola given by the equation: 1æ? y = 2x + 8 -

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Q: Find the vertex, focus, and directrix of the parabola y2 + 6y + 8x + 25 = 0, and sketch its graph.

A: Parabola:         y2+6y+8x+25=0=>y2+2.3y+9+8x+16=0=>(y+3)2=-8x-16=>-(y+3)28=x+2

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

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Q: Find an equation of the parabola with vertex (4,2) and directrix x=-1

A: Find the equation of parabola:

Q: Find the equation for the parabola that has its focus at (-53/4, -7) and has directrix x = 5/4.

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Q: Find an equation for the indicated half of the parabola.Upper half of (y - 2)2 = x - 4

A: Given: y-22=x-4 For finding equation of the upper half of the parabola, we take square root both…

Q: Find the directrix of the parabola.  y^2= -10x

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