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