Question

The centre of a circle is (2 alpha - 1, 7) and it passes through the point (- 3, - 1). if the diameter of the circle is 20 units, then find the value of Alpha.

Answer 1

Step-by-step explanation:

Centre of circle (2α - 1, 7) and radius 10 units

and it passes through (-3 , -1)

Equation of the circle is

${(x - (2 \alpha - 1))}^{2} + {(y - 7)}^{2} = {10}^{2}$

Since, it passes through (-3 , -1), so

$= > (3 + 2 \alpha - 1)^{2} + {(1 + 7)}^{2} = 100$

$= > (2( \alpha + 1))^{2} + 64 = 100$

$= > 4( \alpha + 1)^{2} = 36$

$= > ( \alpha + 1)^{2} = 9$

$= > ( \alpha + 1)^{2} = {3}^{2}$

$= > \alpha + 1 = 3$

$= > \alpha = 2$