Evaluate y ds, where C is the parabola r (3t2, 3t), for 0

Q: 14. Which equation represents the given parabola? O y = -4(x – 4)² + 5 O y = }(x – 4)² + 5 O y =…

A: First option is correct.

Q: For Exercise, find an equation of the form  y = ax2 + bx + c that defines the parabola through the…

A: Consider the given equation of parabola:

Q: Find the following points of intersection. The point(s) of intersection of the parabolas y = x2 and…

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Q: An insect is tracing an elliptical boundary of a hot plate. The ellipse equation is given by+ = 1.…

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Q: Find the length of the arc of the parabola x2 = 4y from x = -2 to x = 2. А. 4.3 В. 4.6 С. 4.9 D. 5.2

A: we have to find the length of the arc of the parabola x2=4y from x=-2 to x=2

Q: 2. Circle the parabolas that are stretches of the graph y = x². а) у3 1.25х? c) y = – x? b) y = 0.25…

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

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Q: 2. Which equation represents the parabola with focus (1, 4) and latus rectum of 4? Oy = 4(a- 1)2 + 3…

A: Here, the parabola is of the form (x-h)2=4a(y-k) Whose focus is given by (h,k+a)=(1,4) given…

Q: The parabola x? – 2x+4y+5=0 has the directrix X=0. True O False

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Q: Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive…

A: let the point on parabola be A= (x, y)  B = (p, 4p) Thus,  AB = x-p2+y-4p2 but parabola is y2=2px…

Q: Which way does the parabola open? (x+ 3 =4 y + 5). h drwn e laft d ninht aun

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Q: he area of an ellipse with axes of length 2a and 2b is nab. The percent change in the area when a…

A: We have to find percent change in the area after increasing major axis and minor axis.

Q: Q3) Using the property of Re z and Im z to show that the hyperbola x2 – y? = 1 can be written as: z2…

A: Given that: Equation of hyperbola is-             x2-y2=1

Q: Where does the line x = 1 + 3t, y = 2−t intersect (a) the x-axis (b) the y-axis (c) the parabola y =…

A: Parametric equations are a set of equations where 2 or more variables are dependent on one single…

Q: Find the value of Y for the hyperbola defined by the equation y² – x² = 7 at the point (3, 4). dx2

A: The equation is y2-x2=7. First find the value of dydx as follows.…

Q: Cоmрute (x + y) dz, where is the portion of the parabola C y = 4 – x2 from -2 to 1+3i.

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Q: Determine the equation of the parabola with the directrix z = 3 and focus (0, 7). O y = 8 (z – 5) O…

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Q: 13. The parabola y = x2 + x + 1 opens: A. To the right %3D B. To the left C. Upward D. Downwarč

A: y=x2+x+1 here parabola is in the form of y=ax2+bx+c which means it can be open up or down…

Q: Q13:- Given a parabola y? P1 tangent to the parabola. Find the area of the triangle A0AB = 4px, and…

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Q: The parabola y=x^2+13 has it's focus at the point (b,c) where  b= c=

A: The given equation of the parabola is, y = x2+13. Also the parabola has its focus at (b, c).Consider…

Q: 2 Write the equation of the hyperbola – 25 · x? + 16 · y² = 400 in standard form + = 1 %3D

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Q: Given the general form of a parabola x2+6x-8y+10=0, what is the y coordinate the focus? (round to 3…

A: Explained below

Q: What is the directrix of the parabola? (x – 4)? = 8 (y + 3) O x = -3 O y = -3 y = -5 x = -5

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Q: Find the evolute of the parabola y=x2.

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Q: Let F(r, y) = (x + 1)7, and let C be the portion of the parabola y = x² that starts at (0,0) and…

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Q: . Find the point on the parabola y = x² closest to (6,3). newor: The noint is (24)

A: Given curve is y=x2

Q: Find the endpoints of the latus rectum of the parabola below. 1 Enter the endpoints as ordered pairs…

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Q: What is the directrix of the parabola? (z+3) =8 (y-1) O y= 3 O y=2 O y= 1 o y=-1

A: If General equation of parabola :  y = a ( x - h ) 2 + k  Then directrix y = k - ( 1/4a )

Q: Find the endpoints of the latus rectum of the parabola below. 1 (v – 1)? 20 (x + 2) : Enter the…

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Q: (x, y)  =           x-intercept (x, y)  =             (smaller x-value) x-intercept   (x, y)  =…

A: We Can make it easier for you.

Q: Find the point P on the parabola y = x? closest to the point (57, 0). (x, V) = ( y y =x 57

A: Let x, x2 be the point on the parabola y=x2 closest to the point 57, 0. Now the distance between x,…

Q: 5.Find the point on the parabola x? = 4y nearest to (0,4).

A: Given:      x2 = 4y    Point : ( 0 , 4 )

Q: 4. Fit a second degree parabola y = a + bx + cx? to the following data 2. 8. 10 y 3.07 12.85 31.47…

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Q: Determine the standard form of the parabola that has the following properties: a) opens upward; b)…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Find the parabola with equation y = ax? + bx whose tangent line at (1, 1) has equation y = 5x – 4. y…

A: Let's find.

Q: Find an equation of the parabola deseribed. Focus at (5, 0); vertex at (0, 0) O y = 20x2 O x = 20y O…

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Q: The value of y dæ – x dy where C is the portion of the parabola y = x² – 1 from (0, –1) to (-2, 3)…

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Q: Find the point on the parabola x = t, y = t2, -∞ < t < ∞ closest to the point (2, 1/2).

A: Given Data The first equation is x=t. The second equation is y=t². The point is (2,1/2).…

Q: ind the vertex and the x-intercepts (if any) of the parabola. (If an answer does not exist, enter…

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Q: . All parabolas with x-axis as the axis and (a, 0) as focus.

A: In this question, concept of differential equation is applied. Differential Equation A differential…

Q: For Exercise, determine whether the transverse axis and foci of the hyperbola are on the x-axis or…

A: The general equation of the horizontal transverse axis hyperbola is given by,

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

A: Converting the equation to standard form

Q: Evaluate x° ds where C is the part of the parabola y = x² from (0,0) to (2, 4).

A: Form the double integral and set the limits than integrate with respect to y and x.

Q: Find the equation of the parabola with focus (-4, 0) and directrix x = 4. a. x? = 16y c. x? = -16y…

A: Given Focus = (-4, 0)  and directrix x=4

Q: Find the coordinates of the vertex for the parabola. Round your answer to 2 decimal places. Include…

A: Given query is to find the vertex for the parabolo.

Q: hat is the shape of the vertical cross section of this solid figure that passes through the vertex?

A: We have to identify the shape of the cross-section.

Q: Evaluate a ds, where C is the parabola i = (3t, 3t2), for – 1 <t < 1. Answer exactly or round to 2…

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Q: Let f(x, y) = x? + 4y. Find the extreme values of f on the ellipse x? + 2y? = 1.

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Q: Which is the equation of a parabola with a directrix at y = 2 and a focus at (5, 0).

A:

Q: For Exercise, determine whether the transverse axis and foci of the hyperbola are on the x-axis or…

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