Show that at a hyperboic poin, he principall direcions bisect the asymptotic directions using The Definitions of the Gauss Map and it's Fundamental Properties.

Q: Draw the hyperbola with the equation: 3x2 − 2y2 + 6x − 8y = 6.

A: 3x2-2y2+6x-8y=6⇒3x2+6x-2y2+8y=6⇒3x2+2x-2y2+4y=6⇒3x2+2x+1-2y2+4y+4=6+3-8⇒3x+12-2y+22=1⇒x+1213-y+2212=…

Q: Integrate counterclockwise dz, C the circle with z2 + 12z + 35 center –5 and radius 2. dz z2 + 12z +…

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Q: What is the image of a horizontal line y = k € R under the mapping W = 2²?

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Q: Describe the image of the line z = 1 + iy under the map flz) = sin z %3D

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Q: What is the equation of the circle with centre (,0) and radius 2? (2a- 1)2 + y? = 2 4. (2x-1)2 + y?…

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Q: b. Calculate its tangent line at (2,0) in the projective plane and verify the result by comparing it…

A: Please find the answer innext step

Q: Consider the curve 2y° + y – y° = x* – 2x° + x². a) This curve has sometimes been likened to a…

A: Given: 2y3+y2-y5=x4-2x3+x2. Graph the curve: The graph of the function represents a bouncing…

Q: 22 - 4y-9x2 = 36 %3D

A: This is a general formula of the 3d parabolic surface. For finding traces points we will use the…

Q: Show that the gradient vector is perpendicular to the tangent at a point of an isovalue curve

A: According to question                                     Let,  w=f(x, y, z)  be a function in…

Q: 2. Find the area of a parallelogram defined by PQ and QR when P = (4, 0, 1), Q = (5, -3, 0), and R =…

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Q: Sketch the locus of points P(x, y) and write down its Cartesian equation given that P is equidistant…

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Q: Fina the are a bounded ナトe fo llo Wing Curves 16-X2.こ0メニ メ33

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Q: 2+9z X =,26+,A

A: Draw the quadratic surface y2+9z2=x using traces. Solution: The traces of the surface y2+9z2=x is…