Is it possible to angle the flashlight in such way that the boundary of the lighted area is a parabola?

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: Write the equation of Spheres with radius R.

A:

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 radius of curvature at any point on parabola y2=4ax

A: Given:  y2 = 4axTo find: The radius of curvature at any point on the given parabola. Formula used:…

Q: At what point does the normal to y = 2 + 2x + 2x² at (1,6) intersect the parabola a second time?

A:

Q: Find the length of a,b,c of the hyperbola: y^2-x^2=1

A: The given equation of hyperbola is: y2-x2=1

Q: Find the radius of curvature at any point on parabola y2=4ax

A:

Q: Find the area of the resulting surface if an arc of a parabola y = x? from (1,1) to (2,4) is rotated…

A: Given curve is y=x2

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: I keep on forgetting how to find the area of a parallelogram.

A: Here we find the are of parallelogram.

Q: Find the area of the resulting surface if an arc of a parabola y = x² from (1,1) to (2,4) is rotated…

A: Given

Q: The arc of the parabola y = 5x2 from (5, 125) to (15, 1125) is rotated about the y-axis. Find the…

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Q: Write an expression for the length of a parametriccurve

A:

Q: Find the standard equation of the sphere with the given characteristics. Endpoints of a diameter:…

A: Solution: The objective is to find the standard equation of the sphere

Q: What is the center and radius of the sphere that has (1, -2, 2) and (3, 4, -12) as endpoints of a…

A:

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: Show that in hyperbolic geometry, the vertices of a triangle can belong to the same circumference.

A: Hyperbolic geometry comes into consideration when surfaces are curved not like surface of a room or…

Q: Determine the focal distance of a hyperbola if the length of the transverse and conjugate axes are…

A: The focal distance of a hyperbola is 17units.

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

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

A:

Q: A reflecting telescope contains a mirror shaped like a paraboloid of revolution.If the mirror is 4…

A: When we draw the parabola  to form the mirror on a rectangular coordinate system  we find…

Q: Determine the area of the largest circle that can be enclosed by the two hyperbolae, xy= 1 and xy =…

A: Solution is here

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: Find the equation of the sphere of radius at centered at (1, 4, 5)

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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: What is the minimum vertical distance between the parabolas y = x² + x en y = x – x²?

A:

Q: Give an example of the reflective property of a parabola.

A: Given:The parabola is the set of points in the plane that are equidistant from a fixed line, (the…

Q: What is the definition of a parabolic cylinder?

A: The parabolic cylinder functions are the solutions to the differential equation d2ydx2 + ax2 + bx +…

Q: What is the maximum area of a rectangle inscribed in the ellipse 25 + y? = 1?

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Q: Find the image of the circle Iz| = 3 under the stereographic projection in the sphere.

A: We let G be a sphere in Euclidean three space. We want to obtain a picture of the sphere on a flat…

Q: In the context of hyperbolic geometry, show that the segment joining the midpoints of two sides of a…

A: Given below clear explanation

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: A mirror for a reflecting telescope has the shape of a finite paraboloid of diameter 0.3 meters and…

A: Equation of a circular paraboloid  f=r24d here, f= focal length along the axis of symmetry from the…

Q: Find equations for the sphere whose centers and radii are given in center(1,2,3) radius sqrt(14)

A: To determine the equation of a sphere.

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: . (a) Show that as (x, y)→ (0, 0) along any straight line y = mx, or along any parabola y = kx², the…

A: Given : f(x) = x³y/(2x^6+y²)  To find : To prove that limit exist along parabola

Q: How is the distance between vertices for hyperbola equal to 2a?

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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: Find the eccentricity of the hyperbola whose transverse and conjugate axes are equal in length. O…

A:

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 geodesic on the surface of a right circular cylinder is a segment of a helix

A:

Q: Find the length of the arc of the parabola x² 4ay measured from the vertex to one extremity %3D of…

A: We can calculate the length of arc using given condition and  formula of length of arc

Q: Please provide solution to the attached question on 3D Geometry.

A: From the given equations of line in Cartesian form, we can write down direction vector and a point…

Q: Which of the fo llowing is a point on the 4) circle whose center is (0,0) and whose radius is 5?

A:

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: Determine the area of the circle whose center is at the origin and tangent to the parabola y = x2 -…

A: y=x2-100from the grapph attached, Parabola cuts X-axis at (10,0) and (-10,0)

Q: Prove analytically that the perpendicular bisector of a chord of a circle contains the center.

A: SOLUTION-