Question

Given below are two statements
Statement I Every homogeneous equation of second degree in x y and z represents a cone whose vertex is at the origin
Statement II If two equations representing the guiding curve are such that the one equation is of the first degree then the required cone with vertex at the origin is obtained by making the other equation homogeneous with the help of the first equation
Choose the most appropriate answer from the options given below

• A. Both Statement I and Statement II are correct
• B. Both Statement I and Statement II are incorrect
• C. Statement I is correct but Statement II is incorrect
• D. Statement I is incorrect but Statement II is correct

Hint:

Homogeneous second-degree equations define conic surfaces, and a cone can be obtained by combining linear and second-degree equations.

Answer 1

The Correct Option is A

A homogeneous equation of the second degree in x, y, and z represents a cone with the vertex at the origin. The second statement is correct, as a cone can be generated by making a first-degree equation homogeneous with a guiding curve equation