The joint equation of the lines through the origin and perpendicular to the pair of lines 3x2 + 4xy – 5y2 = 0 is _______.

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The joint equation of the lines through the origin and perpendicular to the pair of lines 3x2 + 4xy – 5y2 = 0 is `bb(underline(5x^2 + 4xy - 3y^2 = 0)`. Explanation: 3x2 + 4xy – 5y2 = 0 a = 3, 2h = 4, h = $\frac{4}{2}$ = 2 b = –5 If the joint equation of a pair of lines is: ax2 + 2hxy – by2 = 0 Then the joint equation of the pair perpendicular to them is given by: bx2 – 2hxy + ay2 = 0 This is a standard result for lines perpendicular to a pair of lines through the origin. (–5)x2 – 2(2)xy + (3)y2 = 0 –5x2 – 4xy + 3y2 = 0 5x2 + 4xy – 3y2 = 0

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