For some surfaces, the normal lines at any point pass through the same geometric object. What is the common geometric object for a sphere? What is the common geometric object for a right circular cylinder? Explain.

Q: What is the equation of the circle in standard form whose endpoints of a diameter are at A(-5,4) and…

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Q: How do we prove that a shape is a parallelogram using coordinate geometry?

A: We will use the properties of parallelogram to prove this.

Q: What is the equation of a circle that passes through the vertex and the points of latus rectum of…

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Q: Describe in words the surface whose equation is given. p = 5

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Q: X is the center of one circle, Y is the center of the other. How do you know that triangle XYZ is…

A: We will show how the triangle XYZ is an equilateral triangle as following

Q: °. Find the horizontal distance the plane is from the control tower.

A: Here we use basic trigonometric ratios to find out the horizontal distance from tower to the plane.

Q: Choose two figures which are topologically equivalent to each other 25

A: Solution :-

Q: The equation of a family of circles with center (2,k) and radius r that is tangent to the x-axis is?

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Q: A 7.5 10 B 11,3

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Q: x² + + =1 y2 9. 4

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Q: A new building is being constructed a distance of 420 feet from the ocean, and the builder wants to…

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Q: What is the equation of a circle with a center at (4, –9) and a radius of 5? 1- -2 -1 1 2 3 5 9 10…

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Q: What is the standard equation of a circle with center (-2,3), and tangent to the x-axis? 1. (x + 2)2…

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Q: Sketch the given surface

A: Given: x42+y82+z122=1 The given equation is an ellipsoid.

Q: What is the equation for the following circle? center: (12, -1), radius: V209 (-12)2 +(y +1)? = 209…

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Q: find the equation of a sphere with the line segment AB as one of its diameters, where A(-3, 2, 1)…

A: We have to find the equation of a sphere with the line segment AB as one of its diameters, where…

Q: Describe in words the surface whose equation is given. p = 7 O a circular cylinder with radius 7 and…

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Q: Why is the convention "The same scale is used for both axes" most frequently violated when utilizing…

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Q: Use traces to graph and name the surface

A: The given surface is: x24-y29+z216=1...(1)

Q: Find the point where the common point of the circles x2+y2=25 and x2 +y2-12x-6y+35=0 intersects…

A: Here we have to find the point where the common point of the circles x2+y2=25 and x2 +y2-12x-6y+35=0…

Q: find the points on the surface

A: Given, S: x2-y2+6z=0=fx,y,z where normal line to the surface is parallel to the line passing through…

Q: Find the Midpoint of the listed segment using the coordinate plane.

A: The coordinate of E=(-1, 3) and H=(-2 , 0) Here, X1= -1, Y1= 3, X2=-2 , Y2=0

Q: Find the length of the curve 24ry = y' + 48, 2 <y<4 Select one:

A: We have to find the length of the given curve   the given curve is 2xy=y4+48the given interval…

Q: Name the surface and draw an accurate Graph of y = x +z? in R'.

A: The surface is an paraboloid. The general equation of a paraboloid that is symmetrical about the…

Q: What are the coordinates of the center C; and the measure of the radius r of a circle whose equation…

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Q: Find the minimal distance bettween the point Cli4) to the line

A: Definition used -                 Minimum distance from a point to the line -…

Q: Draw and describe the locus of points in the plane that are equidistant from parallel lines l and m.

A: Recall the fact that locus maintain an equal distance from each lines. That is, locus must be half…

Q: 19.) Question is attached!

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Q: What does the cross product of two planes that intersect at a line represent in terms of the line of…

A: Firstly, let us understand what a normal vector is. Normal Vector of a plane is a vector which is…

Q: A surface geodesk represents the equation of a straight line for any surface true O false

A: Solution

Q: Find the point on the surface fx,

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Q: For Fano's geometry, prove that the lines through any one point of the geometry contain all the…

A: Given detail: For Fano's geometry, prove that the lines through any one point of the geometry…

Q: What is the standard equation of a circle with radius 7 and is concentric (same center) with the…

A: Given:- x2 + y2  +2x-4y=5 To find:- Equation of circle concentric with given circle and radius 7

Q: The length of the line segment joining the two points of intersection is 3 – x = y = 7+1 With the…

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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: Two intersecting lines can both be tangents to a circle. O True O False

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Q: Explain why a line in hyperbolic geometry must contain two distinct ideal points.

A: We have to answer given Questions.

Q: Do two points determine a plane?

A: No.

Q: In general if the point of a pre-image is (x, y), what are the coordinates of the image?  Why?

A: Pre-image: An original object with co-ordinates (x, y). image      : An object obtained after…

Q: Write the equation of the circle. Center at (-7, 11), radius 8 O (+11)² + (y-7)² = 121 O (x + 7)² +…

A: We have to find the equation of the circle which has  centre at   ( -7, 11)  and  radius 8. Now as…

Q: Find Sax ds, where C is the line segment in the plane joining (0,0) and (3, 4).

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

Q: Do two intersecting lines determine a plane?

A: Two lines intersect at only one point.

Q: Is this curve a twisted cubic, parabola, line, or helix?

A: The objective is to check whether the curve is a  twisted cubic, parabola, line, or helix.…

Q: Graph the first-octant portion of each plane.x + y = 4

A: Consider the given plane. x+ y=4⇒y=4-x Assume some test points and make a table of values as…

Q: Please answer the questions. Thanks!!! A. Prove that the properties of parallel lines were cut by a…

A: Given

Q: Explain the process you would use to determine the type of intersection that occurs between a line…

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Q: What is the altitude of the plane?

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Q: What is the equation of a circle with center (2, 4) and radius 5? A. (x- 2)2 + (y - 4)² = 5 B. (x+…

A: The standard form of equation of circle is given below: x-h2+y-k2=r2 where, h,k is the coordinates…