Mathematics · JEE | CONIC SECTIONS

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The equation \( x^2 + y^2 - 4x - 8y - 45 = 0 \) represents a circle. Reason (R): Any second-degree equation in two variables \( x \) and \( y \) always represents a circle if the coefficients of \( x^2 \) and \( y^2 \) are equal and non-zero. In the light of the above statements, choose the correct answer from the options given below:

1. A
   Both (A) and (R) are true and (R) is the correct explanation of (A).
2. B
   Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
3. C
   (A) is true but (R) is false.
4. D
   (A) is false but (R) is true.