8.44.) In Ax² + Cy² + Dx + Ey +F = 0, show that if A and C have the same signs, then the graph of the equation is either an ellipse, a circle, or a point, or does not exist. Give an example of each type of equation.

Q: 1. Determine the orthogonal trajectories of the family of ellipses 16x² + 121y? = c. Sketch some of…

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Q: 5. If the receiver is placed at the focus of the satelite dish shaped like a paraboloid which has a…

A: Let's find.

Q: has its vertex at the origin and has directrix at z = 38

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Q: Identify the conic with th e given equa­tion and give its equation in standard form…

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Q: 9. Explain in your own words how to decide what kind of conic it is if you have the equation Ax? +…

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Q: Show that the image of the hyperbola x² - y² = 1 is the transiscate p² = cos24.

A: Introduction: An hyperbola is another significant conic section. It has Cartesian as well as polar…

Q: 7. Determine all values of a that will cause the parabola y=ax² +10x+1 to cross the x-axis at two…

A: 7) y=ax2+10x+1 ...................eq (1) For parabola to cross the x- axis put y=0 0=ax2+10x+1…

Q: A rectangle is to be inscribed inside a semi-ellipse + = 1, -2 <IS2 and 0 y S 3. Give a rough sketch…

A: Solution is here

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: 3. Where do the asymptotes intersect for the hyperbola y = ( 2x +3 ) / ( 8x +5 ) O ( 3/8 , 2/5 ) O…

A: Given : Hyperbola y =2x + 38x + 5   To find the asymptotes.

Q: P1 and P2 are two points on the conic whose angles θ1 and θ2 differ by 180° , show that the h

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Q: 57. Use a change of variables to prove that the area of the ellipse with equation (-) + ) : -1 is…

A: Explanation: Given that, the standard equation of the ellipse is: x2a2+y2b2=1 Solve for…

Q: 1- Sketch the following conic sections: y2 -4y+8-4x² = 0 %3D a-. .2 b- .2 y-4y-4x =8 a 3(y – 5)2 –…

A: As per our company guidelines, we are supposed to answer only the first three subparts. Kindly…

Q: = 1 10 12 = 1 20 12 x2 = 1 100 36 =1 100 144

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Q: Select a possible equation for a parabola with a vertex of (-1,3). Oy = (z + 1) (x – 3) | Oy = (z -…

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Q: Find an equation of the ellipse with foci at (−3,7)and (−3,−3) and whose major axis has length 20.…

A: The foci of the ellipse is (−3,7)and (−3,−3). The length of the major axis is 20.

Q: 1. Find the dimensions of the rectangle of maximum area, with sides parallel to the -1 16 coordinate…

A: Given ellipse is  x2144+y216=1 We need to find the dimensions of the rectangle of maximum area with…

Q: 1.) A gateway is a parabolic shape whose vertex is 20 ft. From the ground, (0,20), and the width of…

A: Given, a gateway  is a parabolic shape whose vertex  is 20 ft. From the ground, (0, 20), and the…

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: 3. Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes…

A: Let vertex of the rectangle be x,y, x,-y, -x,y and -x,-y. Thus, are of the rectangle is fx,y=4xy. We…

Q: the sum of the distances from (x,y) to (-1,0) and from (x,y) to (1,0) is 4. show x and y is related…

A: Distance from (x,y) to (-1,0) is:  Distance from (x,y) to (1,0) is:

Q: State whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

A: 3x2-7y2=z On simplification, we get ⇒z=x213-y217⇒z=x2132-y2172⇒z=x132-y172

Q: For each of the following quadratic equations in x and y, determine which conic section it is.…

A: Let Ax2+Bxy+Cy2+Dx+Ey+F=0 is a quadratic equation.Parabola: If B2-4AC =0 AND A=0 OR C=0Circle: If…

Q: If P1 and P2 are two points on the conic whose angles θ1 and θ2 differ by 180° , show that the…

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Q: 1. Suppose that the equation Ar + Cy + Dx + Ey + F = 0 represents a conic section (nondegenerative…

A: Given: Ax2+Cy2+Dx+Ey+F=0.

Q: 2. Suppose that the equation Ax + Bxy + Cy + Dx + Ey + F = 0 represents a conic section…

A: Suppose that the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 represents a conic section…

Q: A one-way tunnel has the shape of a semi ellipse that is 12ft high at the center and 28H across. a.…

A: If the semi-ellipse is 12ft high at the center and 28 ft across then  The length of the major axis,…

Q: 2. Write the general equation of the parabola with directrix at x FG,-1), and v (. -1). 2

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Q: Compute the length of the latus rectum of the ellipse x2 + 2y2 +4x+ 4y +4=0

A: Given:    x2 + 2y2 +4x+ 4y +4=0

Q: 1. Which Is the corresponding equation of a hyperbola with co-vertices at (0, -6) and (0, 6) and a…

A: Given, The co-vertices of the hyperbola are 0, -6 and 0, 6  and transverse axis is 20 units long.…

Q: 1. Determine the orthogonal trajectories of the family of ellipses 16x + 121y = c. Sketch some of…

A: Given that equation of ellipses 16x2+121y2=cTo find equation of orthiginal trajectarySolution if…

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: Find the maximum area of an isosceles triangle inscribed inside the ellipse x²y² 1, + = a² 62 with…

A: Given problem:- Find the maximum area of an isosceles triangle inscribed inside the ellipse x2/a2…

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 1 –…

A: first we have to draw the sketch of y = 1-x2 and draw a rectangle beneath it From the graph we can…

Q: 4. Determine whether a hyperbola exists if it has an equation of x2 - y2 + 6x +36y = 18.

A: we have to determine whether a hyperbola exists if it has an equation of  x2-y2+6x+36y=18

Q: . The general form of equation of an ellipse is given by Ax + Cy + Dx + Ey +F = 0, where A and C are…

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Q: 1. Determine the orthogonal trajectories of the family of ellipses 16x? + 121y² = c. Sketch some of…

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Q: It has been shown that when like particles with a common charge are hurled at each other, they…

A: Let's find.

Q: What is the standard form equation of the ellipse that has vertices (-1, –17) and (-1,7) and…

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Q: 1. Determine the orthogonal trajectories of the family of ellipses 16x² + 121y² = c. Sketch some of…

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Q: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

Q: 3- The parabola y= ax'+bx+c, mean that the cquation y = ax is .........

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: ) and hyperbola xy = 3 Show thet the ellipse x +3f=3 interseet of right ongle

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Q: From a point P on a rectangular hyper hyperbola at A and B. Show that the a constant, independent of…

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Q: A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating…

A: Let's find how far from the vertex should the bulb be placed.

Q: 6. Show that if m is any real number, then there are exactly two lines of slope m that are tangent…

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Q: 1. Find the point on the parabola y = 3 – x² that is closest to the point (6, 0).

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Q: Find the envelope of the family of ellipses x2/a2+y2/b2=1 having the same area.

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Q: 2. What is the standard form equation of the ellipse with vertices at (0, 6) and (0, -6) and co-…

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Q: 1. Express the following equation in vertex form: y coordinates of the vertex point. 2 = 3x² 12x +…

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