Find Straight Lines Represented By 6x2 + 13xy + 6y2 + 8x + 7y + 2 = 0 And Also Find The Point Of Intersection.

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Question

Find straight lines represented by 6x² + 13xy + 6y² + 8x + 7y + 2 = 0 and also find the point of intersection.

None of these

medium

Solution

Correct option is

Identically. Hence given equation represents a pair of lines.

To find the lines, we rewrite the given equation as

6x² + (13y + 8)x + (6y² + 7y + 2) = 0,

(a quadratic in x)

Solve for x:

Hence lines are 3x + 2y + 1 = 0 … (i)

2x + 3y + 2 = 0 … (ii)

Solve eqs. (i) & (ii) for the point of intersection, we get

Thus lines intersect at point

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