For Exercise, determine whether the transverse axis and foci of the hyperbola are on the x-axis or the y-axis. y? 12 1 18

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: What are the foci of the ellipse? 49 42 O (2+ v7, 1) o (2+ 7, -1) o (tyī, 1) o (12/7, - 1)

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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: 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: 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: 5. Show that the equation represents a sphere, and find its center and radius: x²+y? + z2 – 8x – 10y…

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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: Find the standard equation of the parabola which satisfies the given condition. Focus (7, 11),…

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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

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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: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3. (two…

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Q: For the ellipse b'x' + a'y a'b?, show that the equations of its tangents of slope m

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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: What is the standard equation of the hyperbola if the length of its transverse axis is 12 and one of…

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Q: What is the equation of the directrix of the parabola x2 + 2x+4y– 27=0? A y=8 B y=0 (© y= -2 D y=6

A: Solution ) x2 + 2x + 4y - 27 = 0 Add 1 and subtract 1 in equation  x2 + 2x +1  - 1  + 4y - 27 = 0…

Q: 3 Which equation is for the hyperbola? O x = a (y – k)² + h (z-h)² (y-k)? = 1 O (z – h)° + (y – k)°…

A: LET'S FIND HYPERBOLA EQUATION,   ANSWER :-  OPTION B IS RIGHT   OPTION A IS PARABOLA. OPTION C IS…

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

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Q: Find the center C and the radius r of the sphere S: x2 + y? +z2 + 4x + 8y- 8z =-11

A: General equation of sphere  (x-h)2+(y-k)2+(z-p)2 = r2  center (h,k,p)  radius = r

Q: For Exercise, determine the standard form of an equation of the parabola subject to the given…

A: Given directrix: x=0 and focus (-4,5)The vertex will be the mid point of them Mid point of x=0 and…

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

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

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

A: Given: Corners of the reference rectangle: (8, 7), (−6, 7), (8, −3), (−6, −3); Horizontal transverse…

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 the parabola is F0, 1 and Directrix is y=-1 We have to prove that y=14x2 is 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: 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: What is the shape of the vertical cross section of this solid figure that does not pass through the…

A: Topic:- cutting of surface

Q: Use the figure to complete the sentence below. Y Transverse ais If the center of the hyperbola is…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

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

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Q: (a) Find the evolute of the hyperbola x2 _y? y? =D1 a? b2

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Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: ) Showing in the figure, find the common tangents of the parabola y? = 8ax le 2° + y? = 2a?.

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Q: What is the equation of the standard hyperbola with vertices at (0, t a) and foci at (0, ± c)?…

A: Option B is correct.

Q: 4. Label the focus, directrix, and vertex on the graphs given for the parabolas in Exercises 2 and…

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Q: Determine the standard equation of the parabola opening upward, with focus at (0,6) and whose length…

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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: What is the length of the transverse axis of the hyperbola whose foci are (0,-5) and (0,5), and…

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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: given the directrix of y = 6 and focus of (0,40, which is the equation of the parabola?

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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: For Exercise, determine the standard form of the parabola subject to the given conditions. Focus:…

A: Given:Focus: (0, −3);  Directrix: y = −6

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

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Q: In the conic section r2 36y, what is the distance between the focus and the center? %3D 0 6 O 12 O…

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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: c) Find the center and radius of the sphere whose equation is x² + y? + z? + 10x + 4y + 2z - 19 = 0

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Q: For Exercise, determine the standard form of the parabola subject to the given conditions. Vertex:…

A: To determine the standard form of the parabola.

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

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