Question:
The number of integral values of λ for which
x²+y²+λ x+(1-λ)y+5=0
is the equation of a circle whose radius exceeds 5, is
The number of integral values of λ for which
x²+y²+λ x+(1-λ)y+5=0
is the equation of a circle whose radius exceeds 5, is
Show Hint
Complete squares to identify circle parameters.
Updated On: Mar 20, 2026
- 14
- 18
- 16
- None
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The Correct Option is C
Solution and Explanation
Step 1: Radius squared: r²=(λ²+(1-λ)²)/(4)-5
Step 2: Condition r>5⟹ r²>25.
Step 3: Solving inequality gives 16 integral values.
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