4y2 4x2 4. = 1 9. O 25 a = b = C = - Vertices: Co-vertices: Foci: Standard equation: General equation:

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: Find the standard equation of the parabola with directrix x + 1 = 0, axis y = 1 and the length of…

A: If the axis of parabola is y = 1, then the parabola is horizontal. As we know that the standard…

Q: Graph the line and conic section. r = 4 sec (u + pi/6)

A: General equation of a line is given as y = mx + c, where m is the slope of line and c is the…

Q: Consider the equation x2 + 8x² + z² = 30, then take a cross section when x = 1. Describe the…

A: 6.     Resulting shape gives two parallel line.

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3. (two…

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Q: Write the equation for the hyperbola with foci (1,-5), (9.-5) and conjugate axis of length 6. (x-…

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

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Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

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Q: The orthogonal trajectory of y=cex is a parabola of the form y2=ax+b. Find the values of a and b so…

A: See the details solution in below

Q: 6. y = x + 6x + 4 Axis of Symmetry: Vertex: Sketch:

A: Consider the equation: y=x2+6x+4 Compare the given equation with standard equation, y=ax2+bx+cAfter…

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: sheets of paper for your solutic 1. 49x? – 25y + 98x - 50y- 1201 = 0. a = b = C = (h, k) = Vertices:…

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

Q: 3 r +6 -을V16-(y-2)2

A: Topic - conics

Q: Find the equation of the parabola and put it in the form f(x)= ax^2 +bx+c  Given:  vertex: (7, -4)…

A: Explained below

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3.

A: Given :          The equation of directrix of the parabola is x + 1 = 0          The length of the…

Q: Find an equation of the parabola with vertex (-1,3) and directrix y=7 .

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Q: 2. Alex skated 5 meters in 4 seconds. How fast was Alex skating per second? Answer with supporting…

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Q: 3. Write an equation for the parabola with focus (1, 3) and vertex (0, 3). a. y = 4(x – 3)² b. y =…

A: Given:      focus =1,3      vertex =0,3  The focus and vertex are horizontally aligned, so the…

Q: 2. x = --(y+ 4)² + 5 y Vertex: Opens: Focus: Directrix:

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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: Cartesian

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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: 3z + 3y-18z - 12y + 36 = 0 is the equation of a circle with center (h, k) and radius r for: %3D and…

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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: 2. 4y2+ 169x² – 338x + 32y = 536 Center: %3D Vertices: Co-vertices: Foci: Length of major axis:…

A: Ellipse

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3. (two…

A: The equation of directrix of the parabola is x+1=0. The length of the latus rectum is 3. The…

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: Classify the conic section of each equation.  Explain how you made your decision. 13. 4x2 + 3x = y2…

A: Topic = Conic section   The equation of every conic can be written in the following form:   Ax2 +…

Q: 2. x = --(y+2)² + 7 Vertex: Opens: Focus: Directrix:

A: Given,  x = -14y+22+7   We have to find vertex, opens, focus and directrix. and graph the function.…

Q: What is the equation of the line that contains the vertices of the hyperbola (z+ 4)2 (y+2)² = -1? 16…

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Q: - 4y2+ 169x2 – 338x + 32y = 536 Center: Vertices: Co-vertices: Foci: Length of major axis: Length of…

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Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 2.

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Q: The orthogonal trajectory of y= Ce" is a parabola of the form y = ax+b. what is the value of b so…

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Q: Which conic section is represented by the equation 2x2 + 4x -y + 9+0

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Q: The filament lightbulb is a thin wire that glows when electricity passes through it. The filament of…

A: Given: The given reflector is 7 inches wide and 2 inches deep i.e. (x,y)=(2,3.5)

Q: A hawk flying at 16 m/s at an altitude of 170 m accidentally drops its prey. The parabolic…

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Q: 14. y = 2x- 12x + 10 Axis of Symmetry: Vertex: Sketch:

A: Given

Q: Find the equation of Parabola and Graph with the following information: Center at (0, 0) Vertices…

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Q: 28. Find the directrix for the parabola. (y+ 3)2 + 8 2x x = 4 y = } 7/2

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Q: The circle given by the equation x²+y²+ax+by+c=0 passes through the points (2.0), (-1,7) and (5,-1).…

A: Put given points into given equation

Q: Which conic section is represented by the equation 2x2 + 4x - y+9= 0?

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Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

A: The path of the basketball through from the hoop is modeled by the parabola,

Q: Find the equation of the parabola with directrix y = 3, axis x = 0, and latus rectum 4

A: Given: Equation of directrix:y=3……1Equation of axis:x=0……2Length of latus rectum:4……3

Q: Find the equation of the parabola with directrix x + 2 = 0, axis y = 4, and latus rectum 4.

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Q: 9z-36z-16y-64y+116 0 1) standard equation: (y+ (x+ 2) Center. ( 3) vertices: axis: 4) foci = 5)…

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Q: Find the vertices and foci of the ellipse. x2 + 3y2 + 2x – 6y + 1 = 0 vertices (x, y) = (smaller…

A: Standard form of ellipse x-h2a2+y-k2b2=1 Foci = h±c,k, where c=a2-b2 Vertices = h±a,k

Q: 1. Express the following equation in vertex form: y coordinates of the vertex point. 2 = 3x² 12x +…

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Q: Find b and c so that y = – 10z² + bx +c has vertex (5, 10). b = c =

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