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

Q: Find the family of curve that intersects the family of hyperbolas y² = 2x² +b at an angle arctan(1).

A: To find the family of the curve that intersects the family of hyperbolas y2=2x2+b at an angle…

Q: Find the equation in rectangular coordinates of the quadric surfaceconsisting of the two cones φ =…

A: The relation between spherical and rectangular coordinates in polar form is given by the following…

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

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Q: Find the standard form of the equation of th parabola with: and Focus (-2, 6) Directrix X = 8

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Q: Find the standard equation of the parabola which satisfies the given condition. Focus (7, 11),…

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Q: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

Q: Identify the quadric surface and sketch the graph. z = x2 + 4y2

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Q: Sketch the graph of quadratic surfaces. Y=(x^2+3z^2)^(1/2)

A: We need to plot the surface: y=x2+3z2.

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

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Q: What is the shape of the vertical cross section of this solid figure that does not pass through the…

A:

Q: Find the locus of the foot of the perpendicular from the center of the ellipse x²/a²+y²/b² = 1 on…

A: Let end points of chord be P(acosθ,bsinθ) and Q(acosθ-π2,bsinθ-π2)that is P(acosθ,bsinθ) and…

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

A:

Q: What is the shape of the vertical cross section of this solid figure that does not pass through the…

A: 2)circle

Q: 17. If the focus of the parabola is (-2, 1) and the directrix has the equation x + y = 3 then the…

A: Given Focus of parabola f (-2, 1) Equation of directrix is x+y =3   Here the objective is to find…

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 the points on the ellipse  X^2 + 6y^2 + 3xy =40 With the greatest x coordinator

A: Let us assume thatfx,y=xandgx,y=x2+6y2+3xy-40The lagrange multiplier equations…

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

A:

Q: What is the equation of the line tangent to the hyperbola = 1 at the point (V2a, b)? y = -a+b 26 V26…

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Q: 3x2 − 6x − 4y + 8 = 0 identify the standard form, vertex, focus, ends of latus rectum, directrix;

A: the solution is following.

Q: find center verticals, foci and sketch its graph 2x2+3xy-4y2-3y+1=0

A: We are given : 2x2+3xy-4y2-3y+1=0 Plotting the graph, we have : This graph is a Hyperbola.

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

A:

Q: Determine the relation of the ellipse x + 4y° = 32 and the line 2x +y-1 0.

A: To Determine: the relation between the ellipse x2+4y2=32 and the line 2x+y-1=0 Given: we have two…

Q: It is true that the vertex is halfway between tje focus and the directrix on the principal axis

A: Yes, the vertex is halfway between focus and the directrix on the principle axis

Q: Determine the relation of the ellipse x + 4y = 32 and the line 2x +y-1 0.

A: Step:-1 Given conic and line is x2 +4y2 =32   and 2x+y-1=0 To find the relation between the ellipse…

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: Determine the equation of the parabola using the given information. Focus (0, −3) and directix y =…

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Q: Sketch the parabola y = x² + 2x +1. Use arrows to indicate the maximum and minimum values of y over…

A:

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: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of the parabola is F0, 1 and Directrix is y=-1 We have to prove that y=14x2 is the…

Q: Let 4x^2+3y^2+8x-6y=5 find the center and foci. Graph

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Q: 13.2y – x = 4

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Q: Sketch parabola y = x2 – 10x + 16 by plotting a few points to left and right of the vertex. (Find…

A: Given parabola y=x2-10x+16                  ....(1)

Q: y? =1 (Must show center location, asymptote lines, vertices) |

A:

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: 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…

A:

Q: What are the foci of the ellipse given by (z-3)2 (y-1)2 - = 1? 25 O (-4, 1) and (4, 1) O (3, 5) and…

A: Topic : foci of an ellipse

Q: What is the area of the ellipse x² 16 + y² 9 = 1?

A:

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

A: Given

Q: Choose the equation that represents the graph of the quadric surface below 3 O y = 4 – 5x² – 922 O I…

A: We have given a quadric surface. It is asked to find the equation of the surface from the given…

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

A:

Q: Identify the surface with equation o = = 7

A: Spherical coordinates: The point Pρ, θ, φ represents a point in the spherical coordinates, where ρ…

Q: Find b and c so that y = 7x2 + bx + c has vertex (– 6, 2). - С —

A:

Q: Identify and sketch manually the graph of the quadric surface 25x² -25y² -9z²-150x + 200 = 0.

A: Solution :-

Q: Determine the type of conics for each equation using the discriminant. 20. 5x2 + 2x + 3y - 5 = 0 21.…

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Q: Identify and sketch the graph of the quadratic surface 4x2-y2-z=1

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Q: By differentiating implicitly, find the slope of the hyperboloid 22 + y? – 22 = 1 in the x-direction…

A: We have to find slope of the hyperboloid x2+y2-z2=1 in the x-direction at the points (a) 1,2,2 (b)…

Q: What is the equation of the parabola with vertex at (0, 0) and directrix y = 3 in standard form.…

A: Given vertex 0,0 and directrix y=3. We have to find equation of parabola.

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

A: