Determine the equation of the parabola with the directrix z = 3 and focus (0, 7). O y = 8 (z – 5) O 22 = 8 (y – 5) O (v – 7)? = -6 (z – 1.5) O (z - 7)° = -6 (y – 1.5) %3! O (y - 7) - -16z %3D

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of parabola is F0, 1. Directrix is y=-1. We have to prove that y=14x2 is the…

Q: Find a path in R? whose image set is: (a) The circle with radius 4 and center at (–1,3). (b) The…

A:

Q: 7(t) = a cost i + b sint j,0 <t < 2n is the parametric representation of... (a)circle (b)ellipse…

A:

Q: Find a parametrisation of the hyperbola that is obtained by translating the hyperbola with equation…

A: Here we need to find the effect of translation on parametric equation of hyprabola.

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

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Q: 5. Which equation represents the parabola with focus (1, 4) and latus rectum of 4? O y = (# – 1)2 +…

A: y= (1/4) *(x-1)^2 +3

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: In which direction do the following parabolas open?a. y2 = -4x        b. x2 = 4y

A: Part(a) Given parabola  The graph of the given parabola is

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

A:

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: Find an equation of the Hyperbola that has Foci (-1,–3) & (-1, 7) with asymptotes y = x+ & y = -a+…

A: Standerd equation of hyperboal is (x-h)2a2-(y-k)2b2=1where (h,k ) be the center

Q: Find the equation for a hyperbola centered at (0, 0), with foci at (0, - V 52 -6) and (0, 6). y? x2…

A: Here we have to find the equation of hyperbola having a center (0,0) with foci at 0,-52 and 0,52 and…

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 2) and directrix…

A: Given:            Focus of parabola is : F(0,2)Directrix is:​y=−2.

Q: Find a path in R? whose image set is: (a) The circle with radius 4 and center at (–1,3). (b) The…

A: Let's find.

Q: z' +z+1 Evaluate -dz , where C is the ellipse 4x + 9y = 1. c z² – 3z+2

A: By Cauchy integral theorem,            If the function fz in analytic in some simply connected…

Q: The plane x + y + 2z = 30 intersects the paraboloid z = x^2 + y^2 in an ellipse. Find the points on…

A: Given the plane x + y + 2z = 30 intersects the paraboloid z = x^2 + y^2 in an ellipse. We need to…

Q: 6. What is the equation for the slope of the ellipse+= 1 at (x₁, yi)? A. B. C. D. E. y' = y' = b²y₁…

A: We have to find the equation of the slope of ellipse at the point (x1,y1).

Q: 4. §yʻ dz + 2ry³ dy, where C is the ellipse z + 2y? = 2.

A: To Determine: find the integral  Given: ∮y4dx+2xy3dy where C is the ellipse x2+2y2=2 Explanation: we…

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 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: y? = t2 – 2t and x = t + 2 is I. Ellipse II. Circle III. Parabola IV. Hyperbola

A: topic - conics

Q: Pr. #3) 2 dz - 2y dy, C is part of the ellipse 3r + 2y- 6 from (0, v3) to (-V2,0).

A:

Q: Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1. 1 O f(x) = -- 2…

A: We can derive the equation of parabola as below.

Q: 23 +z+1 Evaluate -dz , where C is the ellipse 4x + 9y² = 1. c z² – 3z +2

A: Consider ∫z3+z+1z2-3z+2dz Singularities of this function are the points at which denominator of the…

Q: F. dr, where C is the ellipse (x + 3)² + 5(y – 2)² = 16 and F(r, y, z) = x²i +y²j+ z²k.

A: The vector field is Fx, y, z=x2i+y2j+z2k. The curve C is x+32+5y-22=16. Obtain the parametric…

Q: Match the ellipsoids shown in the table with the equations. Answer Bank x2 + 2y2 + 2z² = 4 2x2 + 2y?…

A:

Q: How far from the x axis is the focus of the hyperbola (x^2)- (2y^2) + 4x + 4y+ 4 = 0?

A: the given equation of hyperbola is  x2- 2y2+4x+ 4y + 4 =0 it is asked to find how far is focus of…

Q: What is the standard form of the equation of the parabola with the focus (1, –3) and the directrix x…

A:

Q: 'ind a path in R² whose image set is: (a) The circle with radius 4 and center at (-1, 3). (b) The…

A:

Q: Find the equation of the line tangent to the hyperbola x2 −y2 =16 at (5,3).   Give your answer in…

A: The line is tangent to the given hyperbola at (5,3).Tangent line is a straight line.Therefore, the…

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: F. dr, where C is the ellipse (x + 3)² + 5(y – 2)² = 16 and F(x, y, z) = x²i+ %3D Pj+ z°k.

A: Given: x+32+5y-22=16 Fx,y,z=x2+y2+z2

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

A:

Q: Which is the corresponding equation of the hyperbola with foci located at (-8, 0) and (8, 0) and a…

A: Find the equation of hyperbola with given foci and length

Q: 1 Jl جمح The ellipse (4-x) a? (y-k)? = 1 is vertical a. a > b b. a < b +

A: To find the correct option

Q: Q11

A: Just join the centres of two parabolas and draw a line joining them, it is called transverse axis.…

Q: 4. Find the equation of the parabola P with focus F = ( 1,1) and the directrix D: x + y = 0 shown in…

A: --------------------------------------------------------------- dQ,F = dQ,DWhere, dQ,F =…

Q: Q. 40 Consider a hyperbola having its foci at (-4,-1) and (6, 9) and the foot of the perpendicular…

A: Use the following formulae, to obtain the solution. The equation of the line passes through the…

Q: Identify the focus and directrix of the parabola: y = -4(x - 2)² - 3. f: (1, -4), d: y = 2 f: (2,…

A: If the equation of parabola is of the form x-h2=4py-k(i)  if p&gt;0  then focus is h,k+p  and…

Q: 2. Find the equation of the parabola with focus (2, 0) and directrix x = -2. а. b. x' = 8y c. y = 8x…

A: Since you have asked multiple questions according to our company guidelines we are supposed to…

Q: B. Find the general form of the equation of the parabola: 1. With focus Fat (2,7) and directrix e: y…

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

A:

Q: The ellipse x^2/7^2 + y^2/6^2 = 1can be drawn with parametric equations where x(t) is written in the…

A: x272+y262=1since 7&gt;6 S0 major axis on x-axis

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: x, y) u, v) S S u area of the ellipse using the indicated change of variables. 1 V S S 2 u u

A:

Q: What is the distance from the y-axis to the focus of the hyperbola whose equation is (y – 1)? –…

A:

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

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.