Conic Sections — MATHS STD 11 Science — Question

1. g² < c

Solution:

Given:

x² + y² + 2gx + 2fy + c = 0 ......... (1)

The given circle intersects the x-axis.

The equation of circle becomes x² + 2gx + c = 0 ......... (2)

Solving equation (2):

$\therefore$ Discriminant, $\text{D}=\sqrt{4\text{g}^2-4\text{c}}\geq0$

$\Rightarrow4\text{g}^2-4\text{c}\geq0$

$\Rightarrow\text{g}^2-\text{c}\geq0$

$\Rightarrow\text{g}^2\geq\text{c}$

Hence, if g² < c, then the given circle will not intersect the x-axis.