The intersection of a sphere and a plane is always a:

• A) Parabola
• B) Circle (or empty set)
• C) Hyperbola
• D) Point

A right circular cylinder is defined as a surface generated by:

• A) Rotating a rectangle about its side
• B) Translating a parabola along its axis
• C) Rotating a circle about its diameter
• D) Moving a straight line parallel to itself along a curve

Ellipsoid is symmetrical about _____.

• A) (d) All (a),(b) and (c)
• B) (a) xy-plane
• C) (b) yz-plane
• D) (c) xz-plane

A surface is symmetric with respect to the yz-plane if:

• A) Replacing x with −x keeps the equation unchanged
• B) Replacing z with −z keeps the equation unchanged
• C) Replacing x with −x changes the equation
• D) Replacing y with −y keeps the equation unchanged

$$\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{25}} = \frac{{{z^2}}}{{36}},\,\,\,{\text{is }}\,{\text{the equation }}\,{\text{of _____}}{\text{.}}$$

• A) cone
• B) cylinder
• C) paraboloid
• D) sphere

$\frac{{{x^2}}}{{36}} + \frac{{{y^2}}}{{49}} = z$, is an equation of ______.

• A) Hyperboloid of two sheets
• B) Elliptic paraboloid
• C) Hyperbolic paraboloid
• D) Hyperboloid of one sheet

$$\frac{{{x^2}}}{{{3^2}}} + \frac{{{y^2}}}{{{4^2}}} = 1,\,\,\,{\text{is }}\,{\text{the equation }}\,{\text{of _____}}\,\,{\text{cylinder}}{\text{.}}$$

• A) parabolic
• B) elliptic
• C) hyperbolic
• D) circular

$${\text{Trace}}\,\,{\text{of}}\,\,{\text{a cone}}\,\,\,{x^2} + \,\,\frac{{{y^2}}}{9} = {z^2},\,\,\,{\text{in}}\,\,xz - {\text{plane}}\,\,\,{\text{is }}\_\_\_\_\_.$$

• A) $$x = \pm \,\,z$$
• B) $$x = \pm \,\,\frac{y}{3}$$
• C) $$y = \pm \,3\,z$$
• D) no trace

data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAYgAAAAiCAYAAABFs04aAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAeXSURBVHhe7ZvrUVtLEIRJwTGQAjk4BGLwDxIgAzJwBo6ACJwACTgD56B7P4quatq7KwmEdKD6q9rSOfuY7Zl9jJDvvdqVUkopA5ogSimlDGmCKKWUMqQJopRSypAmiFJKKUOaIEoppQxpgiillDKkCaKUUsqQJohSSilDmiBKKaUMaYIopZQypAnizPz582f348eP3dXV1e7bt2+7x8fHl5bLsCU9v3//3n3//v1Zy/X19bO2UsrlaII4Mw8PD7ufP38+P9/f3z9fiJdkS3qY++npaff379/nZ7SVUi7HqwTx69ev529vq8K3POCZ/lsFndLMt9EtQvy2dAluSQ9/1WivbQ32VJPXv+j+OMdffjrfqz3Cue86vY9XCYJgekAJMAdV8OxJZKsJgg2KPn/emla+Jd/e3r68HQaH4aO+4W9JD39F8NfMOWC/s8/ZI/zE1gvla6A17Xq+j38ShJMJgstWF+2WEwR+XPKnkn1wGRNXPo/hoy7kLek5d3IgKehbKJ+8b3VfX5ItnyeRGr/iXxDszX3785Rrtfw3iEwQzpYTBJq3uqHzMj7mMvyIC3lLejw5oOejD/foAmH+m5ubl7cCWz5PgruIO8n5igli37176rV6d4KgnWeK//aon3ZU9C1thGzwqflwkjo5y0LLlqAv7errfVTSnkrq8bbcVMRh1uZwwdGXb6GKBRcO4/QuX1Xk3yEccyFzwcpn/y+Tsu5cemC0Ph4rjzNlFWuQL6uy0kd7ziGNM7Sv/ZBKt87DDMWaT/Ub7S1ddrQBffGDeKsvffyMuZ/qR7vsq91jpriLkRbvT2Fe2VespHMUO/ns/RKNo/DsfmqM14FihA8+nuKxpc3bsTND/bOvx0C2wTXxjCav9/VJ36VfxXG7FN7dlkoyWivIsfjoUDdbm/lJ+B8GeUAcTSYRCi4gyCf0xUxwXnOon6BeGxu8nTZpwIazGge0eTtt8iO14oeeFWj1TUgGXMyKBTpmfd8CfrruFcxPwkpfscGlrL8Y3sMxeoC+iocSGBovBf/mkuuLJt8rjtbf9wBx1nPuO+eYfQ56p01zZp3OGLZ551PPKmj2Op6BsdIDq33u+tyWjycOqhc+DmjTHZHIrsO7NIDmU/wo0pwxBXyiTnOixTU76ps2GKOYgdtT/IF6NHh8ZEvxdP2ug2fZ0nj55W1Am8ckob/HXHPLnuzP1iF5HY0AYe6Ik0I9+L5ZvIwck2BfBJHOMp6+ItvFrB60EdSO1lnfXGyVWUwEiYJ5Vgt5CLM4ZlmRMeP90M2RnEIPbCE5gP+VRSFhUFY/MenAaW0Vk32s9rlsqo1P3zv7zsFoPO+6FIB3t4k97WP1z6L2nH9kHzwW0pR9VtDfNfLu8/q+VQxkP2MCnEEfk34k2V8+ZJGN2f04io/HhvFuT4X+tLmGhH4eoyR95D01upZ9LHvNAgApFFHqy+fKycQD5vPx7M7mJsh2MarHF8ayCN4+swHMN2tbwc83rvNUsPGO1cMljBZdxm/xZ8Zb9JwyOWAH31blWH0kCPbEDF0avvd9vtXhdb05R+5JJ/dongNpYj1gdEHx7tqwp3n27fOcf2Qf/OKZ9Vnh86BJfmKDZ/kH3ubvznsTBPNRN0NzqoiR764Pm+6LkxoSbGBrRvrIs9ZZZOxWvI5ogNg0LlKoC8HB1ULMYDx2FaB01oMM2S6yfvXOXLNNoIU+Bi5ALhnGnfobMnpG/u6Dn5RIWvwPcbON+RaO1bOVvxxmKJmuDg5t9BkdUvYRbftizP6jn18EsstY2p3cv3kOfCzwybv7wfvsvKr/jJx/ZB/wR3ZS0yG4XWnThemxAsVAGjImkJdt+pFkf/mQfibSrXtkFB/sqh0N6Y/wdRmB3dHeE+kjz5pXjGI1Y9kLwzOxKdQdU2A9CARt5Bj1PgfPGsezO8czduUc7R4MkfUjO2qXVvoI1+p9hfd1/ALkZwp+apr5/RawNfJ3H4whaaHnlByjJ5MDcSdG+w7fOUAba3TIf+Kq/aJ+7FUfw34hLgl1vm94zkuCOmzneOo9zsynMwDSpHF88u6xdc2APdez2uc+P5pH9oE218UYfwefcwQ66CNfsKk6RzGQBo+J4so4j7H7MSL7A/2pd6TF69Grd8XHbfGu+EurfAT64ova1BfUBmqjZPzBfWSctHj8aE8/Z7xevRck0ovE8On1TERg9C5xEpb1Cf0QP+o3motPoJ/qfaFUp6JAep3m07hsT63eRhmBTezpAuTbOn19Yd4LsZrFcQVx4zLmIjwlx+hh/oyjr9ul0F8NJFD8WZH7hL1FbH3/zg7eap8L7Gc97xpDvHQGVPKs3t3dvXrPdsZjR+8+n/ejCLeR9hSz1CVcPwUfV+gcCcXc1yY10MfXhr7ejs2MY5L9HY8XRT6kz6rX/Kt9kWO9fbRmQn6kRuFjRcYjtVA3igmMb7uySVhoP9CH8JE/67xFT5lDPDng5XOjC1kJ4zPTBPGFYYN+VHIop6fJ9mvQBFE2DX81sEGbHLaP/9TAxVI+N7Of4D4rTRCllFKGNEGUUkoZ0gRRSillSBNEKaWUIU0QpZRShjRBlFJKGdIEUUopZcBu9x8H3PN42+RJqQAAAABJRU5ErkJggg==.

• A) Only the xy-plane
• B) None
• C) Only the x-axis
• D) All coordinate planes and the origin

${x^2} + \frac{{{y^2}}}{{16}} - \frac{{{z^2}}}{{25}} = 1,$ is an equation of ______.

• A) Ellipsoid
• B) Hyperboloid of two sheets
• C) Hyperboloid of one sheet
• D) Paraboloid

$\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{25}} - \frac{{{z^2}}}{{36}} = - 1,$ is an equation of ______.

• A) Hyperboloid of two sheets
• B) Elliptic Paraboloid
• C) Hyperboloid of one sheet
• D) Hyperbolic Paraboloid

$\frac{{{x^2}}}{{64}} + \frac{{{y^2}}}{{81}} + 1 = \frac{{{z^2}}}{{100}},$ is an equation of ______.

• A) Ellipsoid
• B) Hyperboloid of two sheets
• C) Hyperboloid of one sheet
• D) Paraboloid

A sphere is defined as the set of all points in space that are:

• A) None of these
• B) Equidistant from a fixed point (center)
• C) Lies on a cylinder
• D) Equidistant from a fixed plane

$$\frac{{{x^2}}}{9} + \frac{{{y^2}}}{{16}} + \frac{{{z^2}}}{{16}} = 1,\,\,\,{\text{is }}\,{\text{the equation }}\,{\text{of _____}}{\text{.}}$$

• A) cone
• B) paraboloid
• C) ellipsoid
• D) hyperboloid

Which surface is symmetric with respect to the xz-plane?

• A) data:image/png;base64,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.
• B) data:image/png;base64,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.
• C) data:image/png;base64,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.
• D) data:image/png;base64,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.

$\frac{{{x^2}}}{4} + \frac{{{y^2}}}{9} + 1 = \frac{{{z^2}}}{{16}},$ is an equation of ______.

• A) Hyperboloid of two sheets
• B) Hyperboloid of one sheet
• C) Ellipsoid
• D) Paraboloid

$\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{25}} = z$, is an equation of ______.

• A) Hyperboloid of two sheets
• B) Hyperboloid of one sheet
• C) Elliptic paraboloid
• D) Hyperbolic paraboloid

If the elements of a cylinder are normal to a plane, then it is known as _____ with respect to that plane.

• A) paraboloid
• B) right cylinder
• C) cone
• D) sphere

In cylinder each line through the curve and _____ to the line is called an element (or ruling) of the cylinder.

• A) (b) parallel
• B) (d) both (a) and (b)
• C) (c) center
• D) (a) perpendicular

Which of the following is the equation of a cone?

• A) $$\frac{{{x^2}}}{4} + \frac{{\,{y^2}}}{9} = {z^2}$$
• B) $$\frac{{{x^2}}}{4} + \frac{{\,{y^2}}}{{16}} = \,\, - 3\,{z^2}$$
• C) $$\frac{{{x^2}}}{4} + \frac{{\,{y^2}}}{9} + \frac{{{z^2}}}{{16}} = 0$$
• D) $$\frac{{{x^2}}}{4} + \frac{{\,{y^2}}}{9} = - \,{z^2}$$