Write a MATLAB code to find the equations of the tangent lines of the ellipse x2 + 4y2 = 36 that pass through the point (12, 3).

Q: Find a parametric representation of the solution set of the linear equation.3x − 1/2y = 9

A: Given equation is Where x and y are unknown.

Q: Identify and sketch the conic 4x2 + y2 -8x + 4y - 8 = 0

A: Consider the standard form Ax2+Bxy+Cy2+Dx+Ey+F=0  Here if A=C≠0…

Q: Determine the greatest and least distance from the origin to a point on the ellipsoid 9x2+4y2+z2=36

A: Here is the solution of the given problem. Application of Lagranges Multiplayer.

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

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Q: 15. x2 – 8x + 2y + 10 = 0 Equation:

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Q: Find the equations of both the tangent lines to the ellipse x^2 +3y^2 = 9 that passes through the…

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Q: Find the equation of the conic of major axis on the x-axis, the center at (0,0) passing through (2,…

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Q: Identify the conic represented by equation without using a rotation of axes.

A: Identify the conic represented by equation without using a rotation of axes.

Q: 3. Determine the orthogonal trajectory of the family of parabolas x² – y + 32x = 0. %3D Sketch some…

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Q: Write an orthogonal change of coordinates converting the equation of the conic 3x2+3y +3z+2ry+2rz…

A: Given equation , 3x² + 3y² + 3z² + 2xy + 2xz+2yz = 1

Q: Find the largest and smallest distances from the origin to the conic whose equation is 5x2 − 6xy +…

A: To find the largest and smallest distances from the origin to the conic whose equation is 5x2 − 6xy…

Q: Find the slope of the line tangent to the conic section 25 (x+3), (y+2)² = 1 at (3,8). 36

A: We find the slope of tangent to the given conic with the help of calculus .

Q: Identify the type of conic from the discriminant.Xy-2 = 0 , =45

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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: Find an equation of the line in parametric form that passes through the vertex of the paraboloid…

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

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Q: How are the conics described in terms of a fixed point and a fixed line?

A: We need to describe the definition of conics in terms of a fixed point and fixed line.

Q: Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic.xy + 1 = 0

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Q: Identify the conic represented by the equation x2 + 16y2 - 160y + 384=0 without completing the…

A: we know that equation ax2+by2+2gx+2fy+2hxy+c=0 will represent  ellipse, if h2<ab,…

Q: Determine which of the conic sections is represented by 4x² + 14xy + 5y² + 18x − 6y +30 = 0

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Q: 18 Identify the center of the conic section whose equation is 5x 2 + 9y 2 - 80x + 54y + 221 = 0…

A: Solution is here

Q: Find the equation of the XZ plane.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: What is the relation of conic section to the wall clock?

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Q: Identify and sketch the following conic 4x2 - y2 = 16

A: The solution is:

Q: Identify the type of conic from the discriminant.x2+2ry +y2 + V2x-V2y-2=D0, =45°

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A: Given: Equation of parabola, y=x2+3

Q: 11. Write the equation of the conic section in standard form. 7x² – 3y² – 70x –12y+142 =0

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Q: Show that the “conic section” with equation x2 − 4x + y2 + 5 = 0has no points.

A: Equations for conic sections are obtained as the locus of points following one or a set of…

Q: Find equations of both the tangent lines to the ellipse  x2 + 7y2 = 63  that pass through the point…

A: consider (x0 ,y0) be an any point on ellipse

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

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Q: Show that the line b2xx1 - a2yy1 - a2b2 = 0 is tangent to the hyperbola b2x2 - a2y2 - a2b2 = 0 at…

A: Find dy/dx.Then find dy/dx at the point (x1,y1) by plugging x=x1 and y=y1

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: Use a translation of axes to put the conic in standard position. Identify the graph, give its…

A: Given, 2y2 + 4x + 8y = 0

Q: 64. Find equations of both the tangent lines to the ellipse x² + 4y2 = 36 that pass through the…

A: Given: The Equation of the ellipse is x2 + 4y2 = 36

Q: Find an equation for the conic whose graph is shown. y F (6, 0)

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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: Find the equations of the normal and the tangent to the hyperbola xy + 2x - 5y-2= 0 at the point (3,…

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

A:

Q: Determine the type of conics for each equation using the discriminant. 20. 5x2 + 2x + 3y - 5 = 0 21.…

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Q: 3. Find equations of both the tangent lines to the ellipse x²+4y?=36 that pass through the point…

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Q: Sketch the conic sections. Indicate the foci, and show your work: A) 4x2+3y2+8x-6y=5 B)…

A: A)Given equation is,

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A: We need to prove that if a signal has its source at one focus of an ellipse and meets a point on the…

Q: 3. Find the family of orthogonal trajectories of the family of ellipses centered at the origin and…

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Q: Determine the center of the conic of equation: 16x² + 128r + 49y² + 588y = -1236. A) (4,6) В) (-4,…

A: Brief explanation of the answer is below.

Q: 9. Find equations for two lines through the origin that are tangent to the ellipse 1² – 4x + 4y² =…

A: We have to find

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.