The orthogonal trajectory of y=ce× is a parabola of the form y² = ax + b. Find the values of a &b so that the vertex is at (6,0)

Q: Q 03: find the orthogonal trajectory of family of parabolas represented by the equation y? = 4ax…

A: Given y2 = 4ax2y dydx = 4adydx = 4a2ya = 2yy'4= yy'2y2 = 2xy dydx

Q: The chords of the ellipse 4x2 + 9y2 = 144 having equal slopes of ¾ are bisected by its diameter.…

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Q: 3. Find the coordinates of the foci of the ellipse given by the equation 4x² + y? = 64. O (0, 4v3)…

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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: What are the coordinates of the foci of an ellipse whose equation in standard form 112 x+ is given…

A: We have to find the focci of an ellipse

Q: A nerd guitarist attempted to measure the auxiliary rectangle from the dips of his preloved electric…

A: The standard form of a hyperbola with the traverse axis on the x axis is x-h2a2-y-k2b2=1.  Here h,k…

Q: What is the equation of a parabola with focus at (2,6) and directrixx = 8? %3D O y - 12y + 12z – 24…

A: Equating distance from directrix to distance from focus gives equation of parabola.

Q: The graphs of the conics intersect at two points. x² + y? = 9 = 1 4 What are the coordinates of…

A: To find the points of intersection ,first we find y2 from the two given equations and by  equating…

Q: Which of the following equations represents the parabola with vertex at (3, 2) and directrix y = 4?…

A: To find out the equation of the parabola.

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: What is the equation of an ellipse with its center at (-2, 1), a major axis 16 units long, and…

A: Write equation of parabola

Q: Determine the standard equation of the ellipse. Foci at (-3,4) and (7,4); vertex at (-9,4) Choose…

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Q: What is the equation of the parabola containing the points (0, 5), (–1,9), and (2, 3)? O y = r-z+5 O…

A: The standard form of a parabola is y=ax2+bx+c. The required parabola passes through the 3 points are…

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: The orthogonal trajectory of y=cex is a parabola of the form y2=ax+b. Find the values of a and b so…

A: See the details solution in below

Q: Find the equation of the ellipse with foci and 0, and vertices (0, - 2) and (0,2). O x? y2 1 4 %3! O…

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Q: What is the equation of a parabola in standard form with vertex V(3, – 3) and focus F(3, 2)? A (x-…

A: NOTE: Refresh your page if you can't see any equations. . the vertex is at  and the focus is at

Q: By differentiating implicitly, find the slope of the hyperboloid x² + y? – 22 =1 in the x-direction…

A: Given that: x2+y2-z2=1

Q: The hill has the shape of a cone, which in the XYZ system has the equation z = 4 - sqrt(x^2+y^2) A…

A: Given that hill has the shape of the cone given by z=4-x2+y2 and the tourist moves uphill whose path…

Q: Find b and c, given that the parabola y = x2 + bx + c passes through (0, 5) and (3, 23).

A: (0,5) means when x=0 then y=5. similarly, (3,23) means when x=3 , then y=23.

Q: The figure on the right shows a rhombus centered at the origin, with YR= 8p and PQ - 8s. What are…

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Q: two alpha particles are moving towards each othe as shown at the left. instead of running over the…

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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: Prove that evolute of the ellipsé x2 y? = 1 a? b2 is (ax)2/3 +(by)2/3 = (a² – b²)²/3. %3D

A: Given equation of the ellipse be x2/a2 + y2/b2 = 1 Write the equation of the ellipse in parametric…

Q: An ellipse has its major axis on the x-axis, center at ( -3, 0 ), one of the vertices at ( -5, 0 )…

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Q: 2. Consider the equation r = 4 – y². (a) Find a parameterization of the segment of this parabola…

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Q: Match the parabolas in Exercises 1-4 with the following equations: x? = 2y, x2 = -6y, y? = 8x, y? =…

A: To match the following equations, with the graphs of parabolas and find its focus and directrix,

Q: For Exercise, an equation of a hyperbola is given. Determine whether the transverse axis is…

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Q: Find the coordinates of the four points at which the hyperboloid of one sheet given by x2 y? + 16 z?…

A: This question is related to 3D coordinate geometry, We will solve it using given information.

Q: The graph of y² = x³ is called a semicubical parabola and is shown in the accompanying figure.…

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Q: Show that the ellipse x*/a? + y*/b? = 1 and the hyperbola x/A? – y/B² = 1 are orthogonal…

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Q: A surface in space is defined by the equation -4x? + 16y- 8z2 = 0. Which one of these is true? O The…

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Q: Find the directrix for the parabola. y = 20 (x+ 2)² - 3 1- x= -1 O y = -1 O y = -8 y 3= O x = -8

A: We will find out the required equation of directrix.

Q: Find an equation of the Parabola that has focus 11. (-2,3) and Directrix y = A. (x + 2)² = 4 (y - 7)…

A: Topic:- geometry

Q: Consider the hyperbola of equation: (x – h)² (y – k)2 a2 62 whose foci are (-3, 2) and (9, 2), and…

A: First find distance between foci Then use formula

Q: The orthogonal trajectory of y= Ce" is a parabola of the form y = ax+b. what is the value of b so…

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Q: A landscape architect is designing an elliptical pool that will fit in the center of a 20-by-30-…

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Q: 5b. Solve the problem and upload your work here.* In the accompanying diagram of parallelogram ABCD,…

A: In parallelogram sum of any two adjacent angles must be 180°.

Q: Assume the equation of a parabola and a line are given by y = x +2 x and y =3 x +6, respectively.…

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Q: 28. Find the directrix for the parabola. (y+ 3)2 + 8 2x x = 4 y = } 7/2

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Q: Evaluate y ds, where C is the parabola r (3t2, 3t), for 0 <t< 1. %3D

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Q: For Exercise, write the standard form of an equation of a hyperbola subject to the given…

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Q: By differentiating implicitly, find the slope of the hyperboloid 22 + y? – 22 = 1 in the x-direction…

A: We have to find slope of the hyperboloid x2+y2-z2=1 in the x-direction at the points (a) 1,2,2 (b)…

Q: What is the equation of the directrix of a parabola having vertex at (4, 3) and focus which is 2…

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Q: Find the vertices and foci of the ellipse. x2 + 3y2 + 2x – 6y + 1 = 0 vertices (x, y) = (smaller…

A: Standard form of ellipse x-h2a2+y-k2b2=1 Foci = h±c,k, where c=a2-b2 Vertices = h±a,k

Q: 16. Write an equation of a parabola whose directrix is x = 7 and has a focus at (-3, –7). A. (y –…

A: Since you have asked multiple unrelated questions in a single request we would be answering only the…

Q: Which equation represents the ellipse with vertices located at (3, -3) and (3, -13) and foci at (3,…

A: Ellipse

Q: Find the equation of the Hyperbola whose Foci are at (2,1) and ( 10,1),and the length of its…

A: Given: Foci ≡ 2,1 and 10,1, Length of the Transverse axis = 4

Q: The signal received by a parabolic antenna is concentrated in its receiver, which is placed,…

A: For the Paraboloid,z-axis is it's Principal Axis,Also, it is symmetric with the lines x = 0 (yz…

Q: The equation of the hyperbola whose foci are (-2,0) and (2,0) and length of transverse axis is 2 is…

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