Teaching UP PGT Mock Test Series 2024 Mathematics Parabola, Ellipse and Hyperbola Eccentricity of a conic
A conic equation is ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, where a, b, c, f, g, and h are constants. Then which of the following statements is/are true?
(A). The given conic is a circle if a = 0 and b = 0
(B). The given conic is a circle if a = b ≠ 0 and h = 0.
(C). The given conic is a circle if a = b≠ 0 and h ≠ 0.
(D). The given conic represents a pair of real and distinct straight lines if f = g = c = 0 and h-2 ab > 0
Choose the correct answer from the options given below:
1
(B) only.
2
(B) and (D) only.
3
(A), (B), (C) and (D).
4
(D) only.