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

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: Write the equation of the hyperbola 162? – 4y² – 32z – 32y – 112 = Oin standard form (z – h) (y –…

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Q: b) Consider now the portion of the parabola which is below the line y = 2. Which points have the…

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Q: y? What is the length of the transverse axis of the hyperbola 25 |3D 64 O 8 units 16 units O 5 units…

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

A: According to the given information, it is required to find the maximum and minimum value of the…

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: 10. Which is the equation of a hyperbola with co-vertices at (0, 7) and (0,-7) and a transverse axis…

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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: 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: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given. y? by the…

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

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Q: What is the equation of parabola in standard form with focus F(- 2, – 1) and directrix y=3? A(y-1)2…

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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: 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: 1. Find the minimum and maximum values of f(x,y) : = x²y on the ellipse 4x? + 9y? = 36. %3D

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Q: Find an equation of the parabola that satisfies the given conditions.Focus F(2, 0), directrix x = -2

A: If the coordiantes of the focus h+p,k and directrix x=h-p Then, equation of parabola y-k2=4px-h We…

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

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Q: Sketch the parabola y = x² + 2x +1. Use arrows to indicate the maximum and minimum values of y over…

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

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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: 1. If y varies indirectly as a, and y = 3 when a = 4, what is y when a = 6? %3D y = 2 y = 1 y = 4 y…

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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: 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: The plane x + y + 2z = 6 intersects the paraboloid z = x2 + y² in an ellipse. Find the points on…

A: To find the farthest and nearest point from the origin to the ellipse.

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: 21 Find the equation for the parabola that has its focus at the 2 and has 4 11 directrix at æ = 4…

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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: What are the asymptotes of the hyperbola 9æ? – 4y? – 18æ + 24y + 9 = 0 O (y – 3) = +(x – 1) ㅇ (y-3)…

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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: find a parametrization for the curve. the lower half of the parabola x - 1 = y2

A: Consider the given equation x - 1 = y2 By adding 1 from both sides, ⇒ x = 1 + y2 Let, substitute y =…

Q: 1 in (r', y')-coordinates, if (iii) Find the equation for the hyperbola ry 0 = 1-

A: Find the equation of hyperbola in x'y' system

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

A: Vertices of parabolas = (0,0), Foci on the y-axis.

Q: Find an equation in standard form for the hyperbola with foci at(+8, 0), transverse axis with length…

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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: What is the standard form of the equation of the parabola with the focus (6, –1) and the directrix I…

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Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: Find equetion of Hhe parabole farmm an I with focus zt (3,0) and divectrix x=-3

A: Focus =  F= (3,0)  Directrix - x =-3  i.e. x+3=0

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: 12. Determine the equation of the directrix for the parabola 20x=y2–10y+30 а. X-20 b. y=-20 с. X3-20…

A: Question : Determine the equation of the directrix for the parabola 20x = y^2 - 10y +30.

Q: 7) Determine the shape of the parabola with focus F(7/2,3) and directrix line x=1/2. *

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Q: Describe the graph of the equation. r = 9cos ti – 19sin t j + k O An ellipse in the plane z = 1,…

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