|The length of the latus rectum of the ellipse defined by 25x²+9y² – 300x – 144 y + 1251 = 0 is А. 3.0 В. 3.2 С. 3.4 D. 3.6

Q: Find the points on the ellipse x2+2y2=1, where f(x,y)=xy has its extreme values.

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Q: Find the length of latus rectum of the ellipse 36x2 +25v²+72x-50y-839 = 0: Round off your answer to…

A: The given ellipse equation is 36x2+25y2+72x-50y-839=0. First write the equation in standard form as…

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

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Q: At what point does the normal to y=4x2−(2+3x)y=4x2−(2+3x) at (1,−1)(1,−1) intersect the parabola a…

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Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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Q: Find the equation of the line tangent to the hyperbola x + 2xy - y + x = 5 at the point (3,7)

A: Given,            x2+2xy -y2+x =5 and point (3,7)

Q: Show that the line b2xx1 + a2yy1 - a2b2 = 0 is tangent to the ellipse b2x2 + a2y2 - a2b2 = 0 at the…

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Q: ind the points on the ellipse  5x2 + y2 = 5  that are farthest away from the point (1, 0). smaller…

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Q: A] Find the length of the arc of the semi-cubical parabola y2 x (1,1) and (5,5V5). 8250 between the…

A: Solution:Given        y2=x3    between the points (1,1) and (5,55)To find the Arc…

Q: Find the asymptotes of the cissoid of Diocles defined by the equationy2(2a−x)=x3,a>0.

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Q: Show that line d:3x-4y-5=0 is tangent to hyperbola H:x2-4y2=5 and find the point of contact of the…

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Q: Find the point(s) on the hyperbola x^2 - y^2 = 2 closest to the point (0, 1).

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Q: A] Find the length of the arc of the semi-cubical parabola y² = x3 (1,1) and (5,5V5). between the…

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Q: A baseball is launched into the outfield on a parabolictrajectory given by y = 0.01x(200 - x). Find…

A: Given ------(1)   The average value of a functionon an interval is given by ------ (2) From the…

Q: Q1/ plot x2-y2=z (Elliptic paraboloid) in 3D.

A: Topic:- plot in 3-D

Q: What is the equation of the line tangent to the hyperbola = 1 at the point (V2a, b)? y = -a+b 26 V26…

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Q: Find the equation of one of the tangents to the ellipse 2x² + 4y² = 48 with slope of mt = 1.

A: The given equation of the ellipse is, 2x2+4y2=48 To find the slope of the tangent to the ellipse, we…

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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Q: What is the maximum vertical distance between the line  y = x + 30  and the parabola  y = x2 for…

A: Definition used -                  Vertical distance is given by -…

Q: 3. Find the line normal to the ellipse at X=-1 y= 2+4x-x3

A: Given, y=2+4x-x3 At x= -1 y=2+4-1--13y=2-4+1y=-1 Now point -1,-1

Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

Q: the sum of the distances from (x,y) to (-1,0) and from (x,y) to (1,0) is 4. show x and y is related…

A: Distance from (x,y) to (-1,0) is:  Distance from (x,y) to (1,0) is:

Q: Sketch the graph of the cylinder given by 4x2 + 9y2 = 36. show solution

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Q: What kind of conic section (or pair of straight lines) is given by the quadratic form Q(x1, x2) = x…

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Q: Find the points on the ellipse 3x + y = 3 that are farthest away from the point (1, 0). smaller…

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Q: find the surfase area of ellipsoid obtained by yevoiving the upper-half of the ellipse…

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Q: Find the maximum and minimum values of the function f(, y) = xy on the ellipse given %3D y? by the…

A: Given :  The function f ( x, y ) = x y and the ellipse  x2 + y24 = 1.   To determine :  The maximum…

Q: Find the length of the arc of the parabola y²=4x from the vertex to a point where x=4.

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Q: Compute the length of the latus rectum of the ellipse x2 + 2y2 +4x+ 4y +4=0

A: Given:    x2 + 2y2 +4x+ 4y +4=0

Q: Find an equation of the tangent line to the hyperbola defined by 5x^(2)+4xy−2y^(2)−4x=19 at the…

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Q: Find the mass of a thin plate occupying the smaller region cut from the ellipse x2 + 4y2 = 12 by the…

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Q: If tangent lines to the hyperbola 9x2 − y2 = 36 intersect the y-axis at the point (0, 6), find the…

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Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. What is the point on…

A: We will use Lagranges multiplier method to find optimal solution  To maximize/ minimize f(x,y,z)…

Q: (a) Where does the normal line to the ellipse x2- x   y + y 2 = 3 at the point (1, -1) intersect the…

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Q: Find an +y² equation for the tangent to the ellipse 4 = 2 at the point (2,0).

A: Consider the ellipse, x24+y2=2

Q: Find an equation of the ellipse with foci at (-5,9) and (-5,-10) and whose major axis has length 22.…

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Q: A space probe in the shape of the ellipsoid 4x + y +4z = 16 enters the earth's atmosphere and its…

A: To determine the hottest and coldest points on the probe's surface.

Q: Find the points on the ellipse 2x +y 1 where f(x,y)= xy has its extreme values. %3D

A: Solution:- Here we have to find the extreme value of  f(x,y)=xy subject to constraint…

Q: At what point does the normal to y = 2x2 – (3 + 2x) at (1, –3) intersect the parabola a second time?…

A: Given: y=2x2-3+2x Point: 1,-3 Objective is to find the point where the normal to y=2x2-3+2x at…

Q: Evaluate (x - iy) dz along (a) the parabola y = 2r? from (1, 2) to (2, 8),

A: In the given problem we have to evaluate  ∫C(x2-iy2)dz  along the parabola  y=2x2 from (1,2) to (2,…

Q: Find the volume of the solid formed if we rotate the ellipse+ = 1 about the line 4x + 3y = 20.

A: Calculation of Volume.

Q: Find the maximum and minimum values of f(x, y) 3x+y on the ellipse +25 = 1 %3D maximum value:

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Q: 4x^2 + y^2 = 4 that are the farthest away from point (1,0)

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Q: A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the…

A: Introduction :

Q: Find the point on the curve of intersection of the paraboloid x – y + 2z = 0 that is dosest to the…

A: Here we have to find the point of intersection of the paraboloid x2+y2+2z=4 and the plane x - y + 2z…

Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

A: Given that a person shoots a basketball overhand from a position 8 feet above the​floor, then the…

Q: Sana wants to recycle some elliptic cardboard into rectangular name plates. The minor and major axes…

A: Given problem is : Sana wants to recycle some elliptic cardboard into rectangular name plates. The…

Q: Find the tangent lines as directed. To the ellipse x²+2y²=9 perpendicular to the line 4x-y=6

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Q: Find the parabola y = ax2 + bx + c that passes through (2,1) and be tangent to the line y = 2x + 4…

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