Problems marked (Hyperbolic) are to be done in Hyperbolic geometry (assuming the Hyperbolic parallel postulate and its consequences). (Hyperbolic) Assume that two regular pentagons have the same defect. Prove they must be congruent.

Q: 1. Find the purametric euuatlous of the line that contains the point C,-3,5) and is Perpendicular to…

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Q: Show that the triangle with vertices A(7,8), B(1, 20), C(1, 10) is an isosceles right ti plane model…

A: Given: To explain the given statement as follows, In the upper half-plane model for hyperbolic…

Q: 1. Consider the parabola with focus point (1, 1) and directrix the horizontal line y = -3. a) What…

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Q: Find the distance from the point (0,3,0) to the plane 7x + 4y + 4z = 7. The distance from the point…

A: The Distance between a point to the plane  is given as follows

Q: Which of them are tr 1) Ellipsoid de + 16: Hyperbakid II) =D4- Sy-9 Perbled IV) Sphere

A: The equation of ellipsoid is of the form x2a2+y2b2+z2c2=1 So, (I) is true.

Q: 7. Fill in the blanks: a) The axis of symmetry of the parabola y = -2(x- 3)?– 1 is_ b) When the…

A: Given query is to find indicated points for parabola.

Q: 2. Circle the parabolas that are stretches of the graph y = x². а) у3 1.25х? c) y = – x? b) y = 0.25…

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Q: QUESTION 12 Which of the following polygons can tile the plane? 1: nonsquare rhombus II:…

A: Let us solve the given problem in the next step.

Q: Create one model or figure for a Poinrcare Upper Half-Plane model of hyperbolic geometry.

A: As per the question we have to construct a model for a Poinrcare Upper Half-Plane model of…

Q: Non Euclidian Goemetry Answer the following questions considering the Beltrami-Klein and Poincaré…

A: a) The opposite postulate of the parallels in hyperbolic geometry is known as the "hyperbolic…

Q: A parabola in standard position passes through the point (3,6). What is the equation of its…

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Q: 3. Rewrite each equation below in standard form of a quadric surface and then roughly sketch the…

A: 6-x2+2y2-4y-4z=0x2-2y2+4y+4z=6x2-2 (y2+2y+1-1)+4z=6x2-2(y+1)2+2+4z=6x2-2(y+1)2+4z=4x24-12(y+1)2+z=1

Q: A rod of given length (a+b) unit moves so that its ends are always on coordinates. Prove that the…

A: The two ends of the rod is always on coordinate axes. Let's take one end P of the rod is always on X…

Q: 2. A trucking company needs to determine whether a house trailer will fit that has an opening shaped…

A: In this question we will use basic of calculus i.e concept of parabolic curve. We will first find…

Q: ái) Taka u flection in x- axis shift I unit opew and : y= -2 (x+3)*+1. S -1 -3 -2 -1 Vortical y…

A: topic - domain and range of parabola

Q: 2. Consider the converse statement "If Pis a point such that PA = PB, then Pis on the perpendicular…

A: Please find the answer in next step

Q: Given a sphere in center-radius form, how will you get an equation tangent to only one of the…

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Q: 4. Quadrilateral JKLM is reflected in the x -axis to form quadrilateral WXYZ. What are the…

A: Given, quadrilateral JKLM is reflected in the x-axis to fom quadrilateral WXYZ.…

Q: What kind of figure do you get if you join the midpoints of successivesides of a rhombus? Prove your…

A: We have give a rhombus. AB=BC=CD=AD P,Q,R and S are the mid point side AB, BC, CD and DA…

Q: The figure satisfies the Midpoint theorem for a triangle. Calculate (x + y) 4у x + 4 6(у-1) 4x -2

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Q: If the intersection points of the hyperbola 3x² – y² = 11 and the line 2x + y = 10 are P and Q,…

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Q: 5. What can you change to the two planes to make them parallel? Make as few changes as possible and…

A: given planes π5: 2x-4y+2z-2=0π6: x-y+3z-2=0

Q: Graph including intercepts and all convenient points. 14) 48x2 + 12y2 = 192 Hyperbola

A: Here we find the important points that a hyperbola will help to describe it

Q: Read each question caref (This may include diagrams and equations). 1) In parallelogram MNPQ, QT =…

A: Given query is to find the value of QN.

Q: Quadrilateral RIYA has vertices R (-2, 3), I (3, 8), Y (4, 1) and A (-1, -4). [The use of the set of…

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Q: 3. Use the distance formula to prove that the point (4,2) is on the parabola x = Sy. Prenared hu

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Q: The equation 2x² + 3y² – 5x +3y = 9 defines a c) Parabola d) Hyperbola a) Circle b) Ellipse

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Q: 4) What rule and unit vectors are used to do 3-dimensional graphing? Graph the plane, R = 3x-2y +62…

A: To Explain: The rules of plotting the plane R: 3x-2y+6z=4.

Q: spherical system. (а) (7.07, 45°, 53°) (b) (0.707, 45°, 53°) (е) (7.07, 45°, 35°) (d) (7.07, 54°,…

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Q: Given AABC. AABC is rotated 90º around point R. What are the coordinates of A', the vertex of…

A: Given: A triangle ABC is given. △ABC is rotated 90° around the point R. To find: We have to…

Q: The set of all points x in the plane that satisfy 3x² = 1 + 5x2 is... a) ... an ellipse that is…

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Q: acuce 4. Given J(5, 0), K(8, –11), L(-3, –14), M(-6, –3), determine whether parallelogram JKLM is a…

A: Given  here we have given the coordinated of the parallelogram J(5,0), K(8, -11), L(-3, -14),…

Q: Solve for x. Each figure is a parallelogram. 9) 10) 2x-13 W x+3 T. 9. W A) 11 B) 3 C) 6 D) 2 U 13 A)…

A: Both the quadrilaterals are parallelograms.  There fore their opposite sides are equal.