A parabola is the set of all points in the plane that areequidistant from a fixed point called the and afixed line called the of the parabola.

Q: *5. Prove that no two lines in hyperbolic geometry are equidistant from one another by showing that…

A: To prove that no two lines in hyperbolic geometry are equidistant from one another , first we…

Q: Find a parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it.

A:

Q: A parabola is the set of all points in the plane that are and a equidistant from a fixed point…

A: Given: A parabola is the set of all points in the plane that are equidistant from a fixed point…

Q: If the line X equals three is the axis of symmetry of a para bola , Which coordinates below could be…

A: The axis of symmetry is a line, that divides the parabola into 2 equal halves. For the parabolas of…

Q: Write down the equation of any plane through the origin.

A: Write down the equation of any plane through the origin.

Q: What is the length of the latus rectum of a parabola having its vertex at the origin and focus at…

A: The length of latus rectum of parabola = 4a

Q: In a flat geographic region, the course of two rivers can be represented approximately by the…

A:

Q: Give the maximum number of points at which the following pairs of graphs can intersect. (a) A line…

A: (a) A line and a hyperbola :The maximum number of points at which a line and a hyperbola can…

Q: The set of all points in a plane that are equidistant from a fixed line and fixed point is…

A: The set of all points in a plane that are equidistant from a fixed line and fixed point is a/an…

Q: The set of all points in a plane the sum of whose distances from two fixed points is constant is…

A: We have to fill the blanks The set of all points in a plane the sum of whose distances from two…

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

A:

Q: The set of all points in a plane the difference of whose distances from two fixed points is constant…

A: Given- The set of all points in a plane the difference of whose distances from two fixed points is…

Q: Write the equation of the hyperbola that has a center at (2, – 4), a focus at ( – 2, – 4), and a…

A:

Q: Find an equation of the plane pirpendicular to the line through (2,2,-4) and (9, "1, 3) and…

A:

Q: Prove that the least focal chord of a parabola is its latus rectum

A: Let the equation pf parabola be y2=4ax Focus=(a,0) The endpoint of a chord passing through the focus…

Q: tangent to the parabola y=x^2

A:

Q: A triangle is inscribed in a rectangular hyperbola such that the tangent at one of the vertices is…

A:

Q: Find the standard equation of the sphere that has the points (5, −2, 3) and                  (0, 4,…

A: we know that equation of sphere which has end points of diameter as x1,y1,z1 and x2,y2,z2 is given…

Q: The drone starts at point (0, 0), the landing pad is at point (11, 3) and the parabolic path must…

A: here we know that parabola is passing through three points (0,0), (11,3) and (16,0) and we also know…

Q: The set of all points in a plane that are equidistant from a fixed point is a/an_______ . The fixed…

A: we know that the set of all points in a plane that are equidistant from a fixed point is a…

Q: A __________ is the set of all points in a plane that are equidistant from a fixed line (called the…

A:

Q: Let S be a set of five distinct points in the plane with integer coordinates. Show that the midpoint…

A: Given S to be set of five distinct points in the plane with integer coordinates. Let the coordinates…

Q: Find a parametric representation of a straight line passing through (1,2,1) in the direction of…

A:

Q: Find the equation of a plane consisting of all points that are equidistant from (5,5,-1) and…

A:

Q: What is the distance between the foci of the hyperbola with foci at (2-√13,3)and (2+√13, 3) and…

A:

Q: A hyperbola is the set of points in a plane, the difference of whose distances from two fixed points…

A: Given : A hyperbola is the set of points in a plane the difference of whose distances from two fixed…

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: Which quadric surfaces have both hyperbolas and parabolas as traces?

A: Consider the given: The intersection of a three-dimensional surface and a plane is called a trace.…

Q: On a separate piece of paper, sketch the graph of the parabola y = x + 3. On the same graph, plot…

A: Given: Equation of parabola, y=x2+3

Q: *5. Prove that no two lines in hyperbolic geometry are equidistant from one another by showing that…

A: Hyperbolic Geometry:        It is also a non-Euclidean geometry. It is through a point not on a…

Q: How many arrangements can be made using 4 letters of the word HYPERBOLAS if no letter is to be used…

A: There are total 10 letters in the word HYPERBOLAS. Here arrangement is being considered. So we will…

Q: Show that the set of all points P that are twice as far from (-1,5,3) as from (6,2, –2) is a sphere.…

A: The set of all points P that are  twice as far from -1, 5, 3 as from 6, 2, -2. Let coordinate of a…

Q: A parabola is the locus of a point equidistant from?

A: Answer : A parabola is the locus of a point equidistant from a fixed point and a fixed line.

Q: Find an equation of the plane consisting of all points that are equidistant from (-2, -1, 0) and (0,…

A: Find an equation of the plane consisting of all points that are equidistant from (-2, -1, 0) and (0,…

Q: . Find an equation of a plane passing through the point (3, 4. 0) and containing the line of…

A:

Q: A 24 meter long tension wire is tied firmly between two vertical poles with identical height of 5…

A: To Find:a) Write an equation of the parabola.b)How far is the center of the beam to the wire's 1 cm…

Q: Find an eguation of the sphere that passes through the point (5,-2,-1) whose whose Center is the…

A:

Q: What is a parabola? What are the Cartesian equations for parabo-las whose vertices lie at the origin…

A: Explanation:

Q: A bridge is to be built in the shape of a semi-elliptical arch and is to have a span of 136 meters.…

A:

Q: How to find an equation of a plane through a specific point such as (3,0,3)?

A: There can be infinitely many planes passing through one point and hence you can not find an equation…

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

A: We have to answer given Questions.

Q: Show that the set of all points P, that are twice as far from (-1,5,3) as from (6,2,-2) is a sphere.…

A: Let's find.

Q: The cable of a suspension bridge is in the form of a parabola. The towers supporting the cable are…

A: Given that The cable of a suspension bridge is in the form of a parabola. The towers supporting the…

Q: Find the distance between the point (1,3,-1) and the plane 3x - 4y + 5z = 6. (Enter an exact answer…

A: Given point 1,3,-1 and the plane 3x-4y+5z=6

Q: If a point moves on a plane is such a way that the sum of its distances from two fixed points on the…

A: Let, x,y be a point on the locus.p,q and r,s be two points.distance between x,y and p,q…

Q: Discuss one of the important theorems in hyperbolic geometry for understanding.

A: Hyperbolic geometry, is the geometry that can be used by using all the postulate of Euclid accept…

Q: Find an equation of the plane consisting of all points that are equidistant from (-1, 3, 2) and (2,…

A:

Q: Show that the product of the distances of any point if a hyperbola from it's asymptotes is constant.

A:

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.