I. Graph the curve of an ellipse given its standard form of equation. 1. x2 + y? = 1 25 2. (x - 3)? + (y + 1)? = 1 %3D 16 4 3. (x + 2)? + (y - 4)² = 1 36 9

Q: Situation 6. Find the slope of the ellipse x2 + 4y2 – 10x – 16y + 5 = 0 at the point where y = 2 +…

A: Shown below

Q: 6. What is the equation of the ellipse whose graph is shown below? (1,4) (7. 0) C(1,0) (4, -54 3 A)…

A: Graph of the ellipse is given, we have to find its equation

Q: An ellipse has the equation 16x² + 25y = 40O. Determine the equation of the tangent of the curve at…

A:

Q: 4. Find the focus, directrix and vertex of the parabola (x + 2)2 = 3y - 6, then sketch the curve.

A:

Q: The equation x2-xy+y2=1 describes an ellipse. Find the coordinates (x,y) of all the points on the…

A:

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

A:

Q: 1. What is the equation of this ellipse? -5 --5 10 O (2+2)? (y+4)° 1 81 O 부+ (y 4) 1 -2)2 81 O + = 1…

A: Use the property of ellipse center and major and minor axis.

Q: Find the equation of parabola “y = ax2 + bx + c” passing through points (1, -6), (2, -3), (-1, 0)

A: Consider the given points and the equation of the parabola. Obtain the system of equations with a, b…

Q: What is the equation of the ellipse shown in the graph? y 67 +►X -10 8 -6 -4 -2 0 -2+ 2 4 6 8 10 -44…

A: Major axis: The longest diameter of an ellipse is known as the major axis. It extends from one side…

Q: 2. Sketch and identify the graph of the equation a + y? – 2y –- 3 = 0 in 3D.

A: x2+y2-2y-3=0x2+y2-2y+1-4=0x2+(y-1)2=4The equation represents circle in 2D,but a cylinder of radius 2…

Q: Graph the given ellipse 22 9 + y² 4 1.

A: given equationx29+y24=1

Q: 20. Which is the equation of an ellipse? a) 25 y² 3D1 16 b) x2 + y2 =1 %3D c) 25 x² y2 =D 1 %3D 16…

A: 20)

Q: Find the slope of the ellipse x2 + 4y2 -10x - 16y +5=0 at the point where y=2 + 80.5 and x=7

A:

Q: 1. The ellipse 2x? + 3y2 =4 is drawn below. Find the slope of he tomg ent a+

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: Q3) For what values of n the line y = -x + n intersects the ellipse +=1 at two poin 20

A:

Q: 37. Suppose you go to a company that pays 0.03 for the first day, 0.06 for the second day, 0.12 for…

A:

Q: 6. What is the equation for the slope of the ellipse+-1 at 1 at (x₁, ₁)? A. B. C. D. E. y' = -21 y'=…

A:

Q: 3) A large racetrack can be modeled by the ellipse x2 + = 1, where x and y are measured in…

A: An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the…

Q: Find the equation of the ellipse whose foci are at (7,3) and ( 21,3),and the length of its major…

A:

Q: Find equations for two lines through the origin that are tangent to the ellipse a- 8x +y + 3 =0.

A: We are asked to find the equation of two lines that are tangent to the ellipse.

Q: Determine the relation of the ellipse x + 4y° = 32 and the line 2x +y-1 0.

A: To Determine: the relation between the ellipse x2+4y2=32 and the line 2x+y-1=0 Given: we have two…

Q: Graph the given ellipse. (x – 4)² + (y – 2) = 1 16 6.

A: Given,  (x-4)216+(y-2)29=1

Q: Determine the standard equation of the ellipse. Vertices at (- 6, - 2) and (0, – 2); focus at (- 1,…

A: From the given data  Vertices at (-6 ,-2) and (0,-2)  and focus at (-1,-2)   We have center equal to…

Q: Determine the relation of the ellipse x + 4y = 32 and the line 2x +y-1 0.

A: Step:-1 Given conic and line is x2 +4y2 =32   and 2x+y-1=0 To find the relation between the ellipse…

Q: A parabola has an equation of y² = 4x. Find the nearest distance from the point (-3, 6) to the %3D…

A:

Q: ph the ellipse x2/25 + y2/36=1

A:

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 point on the ellipse x2 + 6y² + 3xy = 40 with the largest x-coordinate (Figure ). -8 FIGURE…

A: Given: x2+6y2+3xy=40

Q: Find the shortest distance from the point (o, 5) to the ellipse 3y? = x³.

A: We will find the the distance from the given problem.  We know      Distance (D) = sqrt {(x-x1)2…

Q: Which of the following equations does not represent an ellipse? * x² + 2y² - 16 = 0 Option 1 x² +…

A:

Q: 24. Construct the equation of a parabola with focus at (-1,2) and a directrix x = -7.

A:

Q: (x-1)° , (y+5)² 2) Graph the ellipse 4 =1 9 +

A: The equation of the ellipse is given by x-124+y+529 = 1 To evaluate : The graph of the ellipse.

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: 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: Find the equation for the ellipse with foci at (-1,3) and (5,3) and whose minor axis has a length of…

A: Given:- The ellipse with foci at (-1,3) and (5,3) and whose minor axis has a length of 4 units. To…

Q: Graph the ellipse. (x – 5)² + (y + 2)² 52 42 y y 10- 10| - 10 -5 10 - 10 -5 10 -5 - 10F - 10 y y -10…

A: As per guidelines, I can answer only three subparts of a question.

Q: Which of the following equations does not represent an ellipse? * x² + 2y² - 16 = 0 Option 1 x² +…

A: topic - equation of ellipse

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

A:

Q: 10) Classify the graph of the equation as a circle, parabola, ellipse, or hyperbola: 4x2 + 25y2 +…

A:

Q: Find the equation of an ellipse with center at (2,-2), vertex at (7,-2) and focus at (4,-2)? O (x +…

A: We have to find the equation of ellipse

Q: Given the ellipse x2/36 + y2/32=1. Determine the distance between foci. (Graph Solution)

A: Given the ellipse x2/36 + y2/32=1. Determine the distance between foci. (Graph Solution)

Q: Find an equation for the ellipse whose graph is shown. y F(0, 2) 2

A:

Q: 4) Find the equation of a parabola which has the focus at (2,9) and the directrix at x=10.

A:

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: Find the slope of the ellipse x^2 + 4y^2-10x- 16y +5=0 at the point where y=2+ 8 0.5 and x-7* O…

A: Given equation of the ellipse is as following: x2+4y2-10x-16y+5=0. We know that the slope of an…

Q: Find the foci of the ellipse (x+1)² (y+5) ² 28 23 + =1

A: We can find the foci in the below steps.

Q: Which is the equation of a parabola with a directrix at y = 2 and a focus at (5, 0).

A:

Q: 4. What is the focus of the parabola whose equation is -(y- 3)2 = (x – 2)? O A. (2, 1) OB. (0, 3)…

A: