First slide

Definition of a circle

Question

$S : x^{2} + y^{2} - 6 x + 4 y - 3 = 0$ is a circle and
$L : 4 x + 3 y + 19 = 0$ is a straight line.

Moderate

A

$L$ is a chord of $S .$
B

$L$ is a chord of $S .$
C

$L$ is a chord of $S .$
D

none of these

Solution

:Centre of S is $(3, - 2)$ and its radius is
$\sqrt{3^{2} + (- 2)^{2} + 3} = 4$
Length of the perpendicular of (3, – 2) from the line L is
$|\frac{4 (3) + 3 (- 2) + 19}{\sqrt{(4)^{2} + (3)^{2}}}| = 5$ Which is greater yhen the radius of
$S$ .So the line L lies outside the circle $S$

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