alleryThe equation of a circle with centre (1, 4) and radius 2 in expanded form is:
Ax² + y² = 4
Bx² + y² + 2x + 8y + 13 = 0
Cx² + y² − x − 4y + 5 = 0
Dx² + y² − 2x − 8y + 13 = 0
Answer & Solution
Correct answer: D. x² + y² − 2x − 8y + 13 = 0
1. The standard form is (x − 1)² + (y − 4)² = 2² = 4.
2. Expand: x² − 2x + 1 + y² − 8y + 16 = 4.
3. Simplify: x² + y² − 2x − 8y + 17 = 4.
4. → x² + y² − 2x − 8y + 13 = 0.
5. So the equation is x² + y² − 2x − 8y + 13 = 0.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 9-11 (pp 227-246, 2019 ed.)._
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