3. Suppose we have Conic described by 2nd-degree equation in the plane : 9y2 + 4x2 = 16 a. Find the Conic representation in projective plane P2 b. Calculate its tangent line at (0,4) in the projective plane and verify the result by comparing it to its Euclidean representation! c. Find and compare the answer with the classical approach through Calculus in Cartesian coordinate

Q: 1. Let l be the line of the extended Euclidean plane through the points P (1,2,3) and Q = (1,1,1),…

A: Note: According to our guideline we will answer the first three subparts of the question as the…

Q: Q.2)(A) Find a formula for the area of the triangle in the xy-plane with vertices at A(0, 0), B(a1,…

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Q: Consider 13 -6v3zy+7y- 256 0. Classify the conic section and (2) calculate the angle of rotation of…

A: Given the equation of the conic section is  13x2-63xy+7y2-256=0                      (i) The general…

Q: Evaluate L₂Lova (4-3²) dydx -√4-x² by using polar coordinates.

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Q: 3. Transform into standard form and identify the conic sections: a) 92²-4y²-36x-24y-35-0. b) x²-3xy…

A: 9x2-4y2-36x-24y-35=0

Q: Let z, and z, be roots of the equation z² + pz + q = 0, where the coefficients p and q may be…

A: Given: Let z1 and z2 be the roots of the equation z2+pz+q=0, where the coefficients p and q may be…

Q: 2) Foci: (2, –5 + V61), (2, –5 – V61) 20 5 Asymptotes: y ==x- 6 3 y-- 5 10 ソ=ーーX 6 3

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Q: 1. (a) Suppose u = 3î+2j-1k and v= 0î+ 55+7k. Simplify the single expression: (u.v) (ux v) (b) Write…

A: We have to solve one question Please repost other questions again

Q: Convert parametric equations to a Cartesian X = tvo cose y = tvosine - gt² 2 X = y = - cost 2 sint +…

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Q: Find the point on the hyperbola x²-9y² 9 where the line 5x + 12y = 9 touches it.

A: Solving                  5x+12y=9  or            y=9-5x12   and   x2-9y2=9  We have…

Q: (a) Find the equations of the tangent planes to the conicoid 7.r2 + 5y + 3z2 = 60, which pass…

A: See the details solution in below

Q: x=-2t and y=2t -1 for -2St<2 Part: 0/ 2 Part 1 of 2 (a) Use the parametric equations to compute x…

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Q: Convert the line determined by the symmetric equations (x + 4) = x(t) = y(t) = z(t) = y-4 -8 to…

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Q: 1) The area of the triangle whose vertices are the points P(1,0,2), Q(3,-1,3), and R(4,1,2). 2)…

A: To find the following equations of line , and area of a triangle.  Since you have posted a question…

Q: 2) x2+12xy-4y2 = 30 Just draw by finding the reduced equation

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Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4…

A: This is the problem from the vector algebra and 3D geometry.

Q: Find a parametric equation for the line through the point (6,5, - 3) and perpendicular to the plane…

A: Given plane is, 7x+4y+4z=15 Since, the line is perpendicular to the plane then the normal vector…

Q: ㅠ ⑤Prove that Imz=0, larg 2 - 11 = 1, Z-Z=0, 12-il = 1Z+il are different equations all describing…

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Q: 6. Find parametric equations for the line of intersection of the planes 2x – y + z = 4 and 3x + y +…

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Q: (x = -1 + sect b) { y = 2 + tant -<< 2 2

A: To convert the given parametric equation to Cartesian form.

Q: Identify and sketch the conic defined by x2 - 2xy+ y² – x – y=0.

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Q: Study and draw the conic section Q(x, y) = 13x² + 13y² — 10xy = 36. -

A: Conic sections (including degenerate ones) are the sets of points whose coordinates satisfy a…

Q: 2. Identify the conic section given by y² + 2y = 4x² + 3 Find its vertex/vertices and focus/foci.

A: We rewrite the equation as: This is an equation of a hyperbola.

Q: The line in R³ through the point Po(xo, Yo, zo) and parallel to the vector v = parametric equations…

A: Given that the position vector of the point is P0 (x0, y0, z0) and parallel to the vector v = (v1,…

Q: Use, 0 = 60°, to write the rotated conic section given below, in the x'y'-plane. x² - y² = 9 Select…

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Q: (x-3)' , (v+1)* 9. 4 36 a) Graph the conic section. b) Name the coordinates of the foci.

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