Find the length of the arc of the parabola x² 4ay measured from the vertex to one extremity %3D of the latus-rectum.

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

A: Basic differentiation is required.

Q: How high is the point P on parabolic arc tunnel of the span of 20ft and height of 16 feet ,at a…

A: Let x be the horizontal distance from the span and y be the height. Therefore top of height of arch…

Q: Find the area of the surface pf revolution geneeated by revolvinh about y= -2 the arc of the…

A: Given, So, x=y212=gy ⇒g'y=y6 limit of y is from 0 to 6 The formula for finding the area is,…

Q: Find the angle at which the parabola y=x2−14 intersects the positive x−axis.

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Q: Show that the center of the osculating circle for the parabola y = x2 at the point (a, a2) is…

A: We need to show that the centre of the osculating circle for the parabola y = x2 at the point (a,…

Q: Find the largest area possible for a rectangle inscribed between the parabola y = 9 – x² and the x-…

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Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: Given vertex is (0 , 0) and focus on negative y axis focal diameter is 2

Q: Find the area of the segment of a sphere formed by revolving the graph of y = √25-x2,0 sxs 4, about…

A: Given y=25-x2, 0≤x≤4 A sphere is a geometrical object that is a three-dimensional analogue to a…

Q: 2. What is the value of y anytime a parabola intersects the x-axis?

A: It is known that the value of y on x-axis is always 0.

Q: .כ Find the ared of a parabola which is inscribed in a rectangle 40 cm long and 25 cm wide.

A: We know are of parabola is( 2/3) ×b×h Where b is base of parabola and h is height of parabola.

Q: 17. Explain the distinguishing feature of the distance between the foci and a point on the eilipse.

A: Here we need to determine the distinguishing feature of distance between the foci and a point on the…

Q: The area bounded by the parabolas (x − 2)^2 − 9py=0 and y^2=9p(x−2) is to be revolved around x = 2.…

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Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: It is given that the Vertex is V(0, 0) The focus is on the positive x axis, 2 units away from the…

Q: Show that the number 4p is the width of the parabola x2 = 4py (p>0) at the focus by showing that…

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Q: Use Green's theorem to find the area between ellipse 16 = 1 and circle x2 + y2 = 25.

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Q: Find the shortest distance +rom the point (0,5)to the ellipse 3 y? = x'

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Q: Find the point on the parabola y = x³ that is closest to the point (1, 2) with two digits accuracy…

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Q: Find the shorted distance from the point A(2, to a point on the parabola y = x². And find the point…

A: Let (x,y) = (x,x2) point on the parabola is closest to A Distance between (2 , 1/2) and (x,x2) is:…

Q: Let LL be a tangent line to the hyperbola xy=8 at x=7. Find the area of the triangle bounded by L…

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Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

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Q: Find the point on the parabola y=x^2 that is closest to the point (6,3) what is the distance between…

A: Given: To find the point on the parabola y=x2 that is closest to the point (6,3) what is the…

Q: Find the point(s) on the parabola x =y closest to the point (0,3)

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Q: Q,9. What point on the parabola y = v2x + 5 comes closest to the ori

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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 80 feet. The…

A: The standard form for the equation of an ellipse with enter (h, k), horizontal major axis of…

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: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 2.

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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 entire length of one arc of the cycloid x=2A-2sinA, y= 2-2cosA.

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Q: Pind Slope of the tangent line @ given pt to the ellipse 9xe + loy? =199 (2,3 313

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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: If a parabola defined by f(x)=2−x2 is inscribed under equilateral triangle ABC, so that the parabola…

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Q: a) Show that the length of the arc of parabola y? =16x measured from the vertex to an extremity of…

A: Given the parabola y2 = 16x.

Q: A rectangle is inscribed with its base on the ?x-axis and its upper corners on the parabola y=2−x^2.…

A: Given, The equation of the parabola is y=2-x2

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

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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: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

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Q: A certain bridge arch is in the shape of the top half pf an ellipse 122 feet wide and 25.6 feet…

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Q: Determine the length of the latus rectum of the curve y² = 8x

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Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

A: NOTE: Refresh your page if you can't see any equations. . The diameter of the dish is 18 feet and…

Q: Find the equation of the parabola with directrix y = 3, axis x = 0, and latus rectum 4

A: Given: Equation of directrix:y=3……1Equation of axis:x=0……2Length of latus rectum:4……3

Q: The parabolic antenna has an equation of y^2 + 8x = 0. Determine the length of the latus rectum.

A: Here we use the standard form of parabola.

Q: A point moves on the parabola 10y = 5x² + 3 in such a way that when x = 6, the abscissa is…

A: To find the increasing rate of ordinate at x=6, differentiate 10y=5x2+3 with respect to time, t,…

Q: Find the shortest distance of the point (10,4) to the parabola y=x2

A: Consider a  point on parabola  y=x2. Distance of this point with (10,4) s2=(x-10)2+(y-4)2…

Q: Find the area of the surface of revolution generated by revolving about the x-axis the arc of the…

A: y2=12x ⇒y=23x ⇒dydx=3x ⇒dydx2=3x2 ⇒dydx2=3x ⇒1+dydx2=1+3x ⇒1+dydx2=1+3x

Q: Find the point P on the parabola y = x2 closest to the point (57, 0). (х, у) %3D ]-«

A: Given the equation of parabolay=x2         ........(1)

Q: How long is the latus rectum of the parabola y? + 3x – 12 = 0? O 12 O 6 4 O 3

A: The given parabola is: y2+3x-12=0

Q: Find the shortest distance of the point (6,3) to the parabola y=x2

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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)