AP EAMCET · Maths · Pair of Lines

If the lines represented by the equation $2 x^{2} - p x y + 2 y^{2} = 0$ are real then the value of ' $p$ ' lies in the interval

A $[- 4, 4]$
B $[- 4, 4)$
C $(- \infty, - 4) \cup (4, \infty)$
D $(- 4, 4]$

Verified Solution

Answer & Solution

Correct Answer

(C) $(- \infty, - 4) \cup (4, \infty)$

Step-by-step Solution

Detailed explanation

As we know, ax2+2hxy+by2=0, represents a pair of straight lines when h2-ab≥0 So, 2x2-pxy+2y2=0 represent pair of straight lines iff p24-4≥0 ⇒ p-4p+4≥0 p∈-∞,-4∪4,∞

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If the lines represented by the equation 2x2-pxy+2y2=0 are real then the value of ' p ' lies in the interval

Step-by-step Solution

If the lines represented by the equation $2 x^{2} - p x y + 2 y^{2} = 0$ are real then the value of ' $p$ ' lies in the interval