Question

(i)
Find the area of the regions into which
the circle x2 + y2 = 4 is divided by the
line x + 13y = 2​

Answer 1

Step-by-step explanation:

Find perpendicular distance from centre of circle which is origin here

$d = \frac{ | - 2| }{ \sqrt{ {1}^{2} + { {13}^{2} } } } = \frac{2}{ \sqrt{170} }$

Now let the angle Alpha ( see diagram)

$\alpha = \sin {}^{ - 1} ( \frac{1}{ \sqrt{170} } )$

Angle that chord makes on centre will be twice so ratio of area will be (2π angle is for total area)

$ratio = \frac{2 \sin {}^{ - 1} ( \alpha ) }{2\pi} = \frac{ \sin {}^{ - 1} ( \frac{1}{ \sqrt{170} })}{\pi} \approx0.2776$