A homogeneous equation of second degree in \(x\) and \(y\) represents which of the following?

A homogeneous equation of second degree in \(x\) and \(y\) represents which of the following?
  1. Two lines
  2. A pair of straight lines through the origin
  3. Only one line through origin
  4. A circle whose centre isn't the origin

Solution

A homogeneous equation of second degree in \(x\) and \(y, a x^2+2 h x y+b y^2=0\), represents a pair of straight lines through origin, provided \(h^2 \geq a b\).

Asked in: AP EAMCET 2020 (18 Sep Shift 1)

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