What is the length of the latus rectum of a parabola having its vertex at the origin and focus at (0,3)?

Q: What point on the parabola y=3−x2 is closest to the point ​(3​,3​)?

A: Basic differentiation is required.

Q: A searchlight is shape like a parabola of a revolution. If the light source is located 2 feet from…

A: Given that , vertex of parabola h,k=0,0 focus of parabola 0,a=0,2 Depth of light y=4 feet Width of…

Q: As arch is in the form of parabola with its axis vertical. The arch is 10m high and 5 at the base.…

A: Topic:- application of geometry

Q: Give the property that defines all parabolas.

A: A parabola is a plane curve and it is mirror-symmetrical and approximately it can be in the shape of…

Q: Given the focus and directrix of a parabola, identify its important characteristics. 10 8 -10 -8 -6…

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Q: What is the length of the latus rectum (LR) of the parabola y = -÷(x – 2)“ + 5?

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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: What is the (unsigned) distance between the vertex and the focus of the parabola given by (x + 4)² =…

A: Given parabola equation,x + 42 = 19y + 5

Q: A bridge is to be built in the shape of a semielliptical arch and is to have a span of 100 feet.The…

A: Given: A bridge is to be built in the shape of a semielliptical arch and is to have a span of 100…

Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2.

A: Let's find differential equation.

Q: The area of the triangle formed by the tangent and the normal to the parabola y = 4ax both drawn at…

A: Given  the parabola y² = 4ax both drawn at the same end of the latus rectum and the axis of the…

Q: Determine the equation in standard form of the parabola that satisfies the given conditions…

A: Given that :

Q: 2. Parabola with x+1= 0 as the directrix, y = 1 as the axis, and the length of the latus rectum is…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: What is the equation of the parabola with axis parallel to the x-axis, whose vertex is at (-1,7) and…

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

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Q: A parabola has its axis parallel to the x-axis, one end of its latus rectum at (-15/4,3/2) and…

A: Given Information:A parabola has axis parallel to the x-axis.Latus rectum at -154 , 32Vertex at (-1,…

Q: Find the length of the arc of the semicubical parabola x  sq = ycu . betweenthe points (2,2 )  ; (4,…

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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: 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: Consider a parabola that intersects the x-axis at points (-1, 0) and (3, 0).

A: We need to find an equation of parabola that intersects the x-axis at (-1, 0) and (3, 0). Thus,…

Q: What is a parabola? Describe its shape.

A: We have to define parabola and describe it shape.

Q: Suppose that point A(-4,0) lies on a parabola whose focus is at (5,3). What is the length of the…

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Q: What point on the parabola y=(6−x)2 is closest to the point (6​,6​)?

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

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Q: Find the standard form of a parabola with the following properties: Center at the origin…

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Q: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

A: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

Q: A parabola with a negative latus rectum has endpoints at (5, 1) and (5, -11) Where is the vertex? *

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Q: A rectangular object 25 m wide is to pass under a parabolic arch that has a width of 32 m at the…

A: The arch can be modeled by the vertex form of a parabola centered at the origin with the base being…

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: Define the term parabola?

A: Given: The term parabola.

Q: A pair of buildings on a college campus are shaped and positioned like a portion of branches of the…

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Q: Show that the product of the distances of any point of a hyperbola from its asymptotes is constant.

A: We have to show that the product of the distances of any point of a hyperbola from its asymptotes is…

Q: Find the standard equation of a parabola if its latus rectum measures 9 units, axis at y = 3, p is…

A: Let's find standard equation of a parabola.

Q: What is the maximum area of a rectangle inscribed in the ellipse defined by x2/64 + y2/25 = 1? Enter…

A: Let the length and breadth of the rectangle as x, y respectively Area of rectangle = xy Now…

Q: Find the minimum distance between the point (5,1) and the parabola y=-x2 ?.

A: Find the minimum distance between the point (5, 1) and the parabola y = -x2?

Q: Find the standards form of the equations of the below parabolas with the given characteristics.

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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: Show the figure or model of a rectangular object 25 m wide is to pass under a parabolic arch that…

A: given that Parabolic arch has a width 32m at the base and height 24m at the center Vertex of…

Q: [1] What is the c value of a parabola with a Vertex of (4,2) and a Focus of (4,4)?

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: A parabola with directrix y = -1 and one endpoint of the latus rectum at (-1,3)

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Q: Find the length of the latus rectum of the parabola x2 = 4py. Then find the length of the parabolic…

A: Given , Equation of parabola  x2 = 4py     Comparing with the Standard Equation of Parabola  x2=4ay…

Q: Find the DE of parabolas with vertex and focus on the x-axis.

A: We know that equation of parabola when vertex and focus on the x-axis is, y2=4ax-h  where a and h…

Q: · Write an equation for the parabola with vertex at (4, –1), opening upward, and with a vertical…

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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: A cable durpended between two Do po has a Jag of 1. 20 meters apart a form of a parabola, find its…

A: The distance between the pole = 20 m and the sag of 112 m=32 m. We have to find the equation of the…

Q: which satisfies th

A: Parabola: The focus of the parabola is (-2,-5) The directrix x=6 The general form of parabola is…