Question:
If \( x^2 + y^2 + 2gx + 2fy + 1 = 0 \) represents a pair of straight lines, then \( f^2 + g^2 \) is equal to
If \( x^2 + y^2 + 2gx + 2fy + 1 = 0 \) represents a pair of straight lines, then \( f^2 + g^2 \) is equal to
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Memorize condition: circle becomes pair of lines when \(g^2+f^2=c\).
Updated On: May 1, 2026
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The Correct Option is B
Solution and Explanation
Concept: Condition for pair of straight lines:
\[
g^2 + f^2 = c
\]
Step 1: Compare given equation with general form: \[ x^2 + y^2 + 2gx + 2fy + c = 0 \]
Step 2: Here \( c = 1 \)
Step 3: For pair of straight lines: \[ g^2 + f^2 = c \]
Step 4: Substitute: \[ g^2 + f^2 = 1 \]
Step 5: Hence answer: \[ f^2 + g^2 = 1 \]
Step 1: Compare given equation with general form: \[ x^2 + y^2 + 2gx + 2fy + c = 0 \]
Step 2: Here \( c = 1 \)
Step 3: For pair of straight lines: \[ g^2 + f^2 = c \]
Step 4: Substitute: \[ g^2 + f^2 = 1 \]
Step 5: Hence answer: \[ f^2 + g^2 = 1 \]
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