Please explain the following.....how it's working.
Suppose a curve 3x2-y2-2x+4y=0 has all chords subtending a right angle at the origin.
Let equation of chord be lx+my=1
To make the equation of the curve HOMOGENEOUS
3x2-y2-2(x-2y)(lx+my)=0
or,(3-2l)x2+(4m-1)y2+(4l-2m)xy=0......(1)
First question , what is homogeneous eqn. and what is the need to make the eqn. of the curve homogeneous ?
2nd. It is said that eqn.(1) represents two perpendicular lines....whatdoes it mean....basics?
3rd. hence show that all the chords subtending a rt. angle at the origin are concurrent.
Please clear the basics on which this question stands ?
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1 Answers
1for 1st question-
A rational, integral, algebraic equation of the variables x and y is said to be homogeneous equation of nth degree in x and y, when the sum of the indices of x and y in every term is the same and is equal to n...
for 2nd question-
just read the theory of pair of st lines from any book and u will get the answer...
