Write the equation of the ellipse 25x + Yy² + 50x + 72y - 56 O In standard fo (x- h)? (y – k)? = 1. a2 62 where: h = k = a = 9.

Q: Write the equation of the hyperbola 36x? – 25y? + 288x – 150y – 549 = 0 in standard form (x – h)?…

A:

Q: What is the general form of equation of an ellipse if its center is at (3,-1), a = 4, b = 3 and its…

A: The standard form of an ellipse is [(x – c1)2 / a2 ] + [(y- c2)2 / b2 ] = 1 Where (x, y) –…

Q: 5. Find the maximum and minimum values f(x, y) = xy can take on the ellipse 4x²+y? = 16.

A: The given function f(x,y)=xy to the ellipse 4x2+y2=16

Q: What is the standard form of the parabola, y + 2x + 10y + 9 = 0, given in conic form?

A: Do some rearrangement in the equation of given conic to convert it in standard form of equation

Q: Write the equation of the hyperbola 4x2 – 25y? + 8x + 250y – 721 = 0 in standard form (x – h)? (y –…

A:

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

A:

Q: Write the equation of the ellipse 16x? + + 4y“ + 64x + 32y + 64 = 0 in standard form h)? (x (y – k)²…

A:

Q: Find the maximum and minimum values f(x, y) = xy can take on the ellipse 4.x?+y? = 16.

A: Here we have to find maximum and minimum value of given function.  The solution is in 1st and 2nd…

Q: Write the equation of the ellipse 16x? + 9y? + 160x – 90y + 481 = 0 in standard form %3D (æ – h)? (y…

A:

Q: Find an equation for the conic whose graph is shown. y 10 5 K11, 0) 10 15

A: Given,

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: Write the equation of the ellipse 9x2 + 25y² – 54x – 50y – 119 = 0 in standard form (x – h)² (y –…

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

A:

Q: 22. The equation x2 + BX + y + Cy + D = 0 is: A. Hyperbola B. Parabola C. Ellipse

A: The standard form of equation of a conic section is Ax2+Bxy+Cy2+Dx+Ey+F=0 where A, B, C, D, E, F are…

Q: 0 = 3x2 – 6x+4y² – 16y+18 is an ellipse. True False

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Q: Find the points on the ellipse x^2 + 9y^2 = 9 and the line x + y = 10 that are closest and farthest…

A: Distance between the two points: - The length of the line segment connecting two places is called…

Q: Write the equation of the ellipse 4x + 9y + 72x + 108y + 612 = 0 in standard form. O (e+9)² + (y+6)°…

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Q: Write the equation of the ellipse 4x² + 25y? – 40x + 150y + 225 = 0 in standard form %3D (x – h)?,…

A:

Q: 7. Write the equation of the ellipse in standard form. 8x +32x + 4y – 8y = -4 (+2)2 4 (y+1)? =1 8 O…

A:

Q: Write the equation of the ellipse 25a? + 36y² + 150x – 72y – 639 = 0 in standard form (x – h)? (y –…

A: Wr have to write the ellipse equation in standard form .

Q: 1. For the parabola equation: (y-2) = -3(x+4)^2 + 7, in which direction does the parabola open? *

A: We have to find the direction in which the given parabola opens.

Q: Find the points of intersection between the line 4y - 3x + 12 = 0 and the ellipse 9x 2 + 16y 2 =…

A: The line 4y-3x+12=0 And the Ellipse 9x2+16y2=144 We need to find the intersection point of the line…

Q: Find the maximum and minimum values of the function f(, y) = xy on the ellipse given %3D y? by the…

A: Given :  The function f ( x, y ) = x y and the ellipse  x2 + y24 = 1.   To determine :  The maximum…

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

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Q: Find the evolute of the ellipse x2 / a2+y2 / b2=1.

A: The given ellipse has the equation:

Q: 8) Write the following equation in standard form for an ellipse. * 4(y+ 1)² + 7(x – 1)² = 28 (x –…

A: Given 4y+12+7x-12=28

Q: The equation x2 − xy + y2 = 3 represents a “rotated ellipse”, that is an ellipse whose axes are not…

A: Given: The equation x2 − xy + y2 = 3 represents a “rotated ellipse”, that is an ellipse whose axes…

Q: Write the equation of the ellipse 25x² + 9y – 250x + 36y + 436 = 0 in standard form (x – h)? (y –…

A: We use completing the square method.

Q: Given the ellipse 16x2 + 25y2 – 64x – 50y – 311 = 0, determine its center. a. (1,2)             b.…

A: Note that the standard form of the equation of the ellipse is given by: (x-h)2a2+(y-k)2b2=1...(1)…

Q: Write the equation of the ellipse 36x2 + 16y² – 216x + 160y + 148 = 0 in standard form %3D (x – h)?…

A: 36x2+16y2-216x+160y+148=036x2-216x+16y2+160y=-14836(x2-6x)+16(y2+10y)=-14836(x2-6x+9)+16(y2+10y+25)=…

Q: Write the equation of the ellipse 36æ² + 4y? + 72x + 32y – 44 = 0 in standard form (x – h)? p2 (y –…

A:

Q: (-3x) dxtxdy C is part of the ellipse 5x2+6y=30 fromC0,-V5) to cra,O). X,

A: Line integral Given ellipse is  From .

Q: Find the extreme values of f(x, y) = e¬¤y for the points on the ellipse x² + 4y? = 1

A:

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: Which conic section is represented by the equation 2x2 + 4x -y + 9+0

A:

Q: Let 49x + 25y 2- 294x - 250y- 159 = 0 (2 – h) (y – k)? = 1. - - then write the ellipse in standard…

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Q: the graph of the equation X+kxy + 49y = 7 where k is any positive constant less than 14, is an…

A: Here comparing given equation with standard equation of graph

Q: Write the equation of the ellipse 9a²+ 16y² – 90x – 32y + 97 = 0 in standard form a2 (x – h)? (y –…

A:

Q: Identify the type of conic section from the equation: y^2 - 4y - x^2 6x =12

A: We have been given the equation  y2-4y-x2+6x=12

Q: Find the equation of the minor axis of the ellipse x² +4 y -8x-8y= 44 Select one: Oy = 1 Oy=3 O None…

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Q: Q9: Show that in an ellipse b2 = a² (1 – e? ).

A:

Q: The equation of the parabola r = 4(y– 2)² is opening

A: Note: Equation of parabola Direction where it opens y=ax-h2+k and a&gt;0 Upward y=ax-h2+k and…

Q: Write the equation of the hyperbola 25z – 16y + 150z + 64y- 239 = 0 in standard form %3D (2 - h) (y-…

A: Equation of hyperbola 25x2+ 150x-16y2+64y-239= 0 25( x2+6x)-16(y2-4y)= 239…

Q: 5. What is the standard-form equation of the ellipse shown? -2- x2 1 25 %3D 16 1 %3D x2 25 1 16 O x2…

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Q: Write the equation of the ellipse 9x? + 25y? + 90x + 200y + 400 = 0 in standard form (x – h)? (y –…

A: See the details solution in below

Q: Write the equation of the hyperbola 25z - 16y + 150z + 64y – 239 = 0 in standard form (z – h) (y-…

A: Equation of hyperbola 25x2-16y2+150x+64y-239=0 25x2+150x-16y2+64y=239 25(x2+6x)-16(y2-4y)= 239…

Q: 2. Which equation represents a parabola with vertex (4,4) and directrix y = 2? Oy=2x² - 4x + 4…

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Q: Find the equation of the parabola y = ax^2 + bx +c that passes through the points (-1,-4) (1,4), and…

A: topic  -  parabola

Q: 4. (a) Derive the equation of the ellipse z+=1 b² =1. a

A: We need to derive the equation of an ellipse centered at (0, 0) with foci at (-c ,0) and (c, 0) and…

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.