caculate and generate the graph of following general cylinders and surfaces in three dimensions. 1.9x^2 + 4y^2 =36 2.z=16-x^2 3.9x^2 + 4y^2 +z^2 =36 4.9x^2 + 9z^2 - 4y^2 =36

Q: Find the points on the ellipse                  x^2/a^2+y^2/b^2=1 such that the tangent at each…

A: Let P be (acosθ, bsinθ), then the equation of tnagent at P is         xacosθ+ybsinθ=1Slope of…

Q: find the latus rectum of the hyperbola 4x^2-y^2-32x-4y+24=0

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Q: Consider the following equation of a quadric surface 9x^2 - 81y^2 - (z^2/4)=0 (a) Find the…

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Q: A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/20^2 + y^2/12^2 = 1. The…

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Q: A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/22^2 + y^2/10^2 = 1. The…

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Q: - The surface 5x^2 + 2z^2 = 3y is heading towards which axis? - Identify the surface generated by…

A: 5x^2 + 2z^2 = 3y x= 3n1 ,  y = -3(5n12 + 2n22) , z = 3n2

Q: the sum of the distances from (x,y) to (-1,0) and from (x,y) to (1,0) is 4. show x and y is related…

A: Distance from (x,y) to (-1,0) is:  Distance from (x,y) to (1,0) is:

Q: The length of the latus rectum for the ellipse x^2/64 + y^2/16 = 1 is equal to

A: Explanation of the answer is as follows

Q: Find the transverse axis of the hyperbola whose equation is: x^2/4-y^2/9=1x^2/4-y^2/9=1 Group of…

A: Given equation of hyperbola x24-y29=1 key points   ;  The transverse axis is the axis of a hyperbola…

Q: the midpoint of line segment with end points (-1,6,2) and (3, 2, -4) What is the distance between B…

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Q: Why are 9x^2-81y^2=0 and 9x^2-(z^2/4)=0 hyperbolas that pass through the origin and not lines that…

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Q: Find the foci of the following hyperbola: (0+1)² (x-1)² = 1 O (-1+√34,-1); (-1- √34,-1) O (1,4); (1,…

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Q: What is the equation of the ellipse with the center at (0,0) that passes through the points (2,0),…

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Q: Sketch the graph of the equation in xyz coordinate system and identify the surface 8x? + 4y? – z2 =…

A: Sketch the graph for the given surface.

Q: Find the trace of the surface 4x^2 − y^2 +6z^2 = 2 in the yz-plane and identify the conic section.

A: Given 4x2-y2+6z2=2

Q: Find the point on the sphere x^2+ y^2+ z^2= 9 farthest from the point (-1,-1,1).

A: To find the point on the sphere  that is farthest from the point , we can use the property that the…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.