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11th Standard Maths Two Dimensional Analytical Geometry
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Prove that the straight lines joining the origin to the points of intersection of 3x2+5xy-3y2+2x + 3y = 0 and 3x - 2y - 1 = 0 are at right angles.

Accepted Solution

A:

Given equations are 3x2 + 5xy - 3y2 + 2x + 3y = 0 ..(1)
and 3x - 2y - 1 = 0 \(\Rightarrow\) 3x - 2y = 1
Homogeneous equation (1) with (2) we get,
\(\Rightarrow\) 3x2 + 5xy - 3y2 + 2x + 3y0(1) = 0
\(\Rightarrow\) 3x2 + 5xy - 3y2+ (2x + 3y) (3x - 2y) = 0 [using 2]
\(\Rightarrow\) 3x2 + 5xy - 3y2 + 6x2 - 4xy + 9xy - 6y2 = 0
\(\Rightarrow\) 9x2 + 10xy - 9y2 = 0
Since sum of the co-efficient of x2+Co-efficient of y2 = 9 - 9 = 0.
∴ The lines are at right angles and passing through the origin.

Dear Students Great you got the answer for your question,

Prove that the straight lines joining the origin to the points of intersection of 3x2+5xy-3y2+2x + 3y = 0 and 3x - 2y - 1 = 0 are at right angles.

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