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Every conicoid has a unique centre.

Is the statement true? Give reason for your answer, either with a short proof or a counterexample.
ax^2+ by^2+ cz^2= d
represents a sphere with radius
√( a^2+b^2+c^2-d) where a,b,c,d are positive real numbers.


Is the statement true? Give reason for your answer, either with a short proof or a counterexample.
Given any two conics C1 and C2 , at least one element of R× R will belong to C1 ∩C2


Is the statement true? Give reason for your answer, either with a short proof or a counterexample.
Any curve in 2D that is symmetric about the origin is also symmetric with respect to both the axes.

Is the statement true? Give reason for your answer, either with a short proof or a counterexample.
Every cylinder has a circular base.

Is the statement true? Give reason for your answer, either with a short proof or a counterexample.
Draw a Venn diagram of sets A, B and C where A ⊆ B, A ∩ C ≠ φ, B∩ C = φ
What is the universal set you have chosen? Justify your choice of sets in the diagram.
Find the roots of the equation
2x^3-x^2-22x-24=0
if two of them are in the
ratio 4:3 .
Obtain the discriminant of the equation 2x^3-23x^2+82x-78=0
Hence provide the nature of its roots.
Find the polynomial over R of least degree which has i−3 and √7+5i as its
roots.
x/5=80%. Which number makes this true?