Question

Find the diameter of the
circle whose centre is (-4,2) and passes through
(-1,-2)​

Answer 1

Tip

To solve these types of questions, distance coordinate formula is used.

Distance formula is used to find the distance between coordinates of two points. The distance between the points $(x_1,x_2)$ and $(y_1,y_2)$ is given by:

$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Step - 1

Given: Diameter of the circle whose centre is (-4,2) passes through (-1,-2).

To find: Diameter of the circle.

Let us assume the centre point as:

$O(-4,2)$

Let $A(-1,-2)$ be any point of the circle.

Step - 2

Radius of the circle is the distance from its centre and a point at the end of its arc. We can observe that OA is the radius of the circle.

Let us use distance formula to find the radius of the circle.

$OA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$OA = \sqrt{[(-1) - (-4)]^2 + (-2 - 2)^2}$

$OA = \sqrt{(-1+4)^2 + (-2 - 2)^2}$

$OA = \sqrt{(3)^2 + (-4)^2}$

$OA = \sqrt{9 + 16}$

$OA = \sqrt{25}$

$OA = 5\:units$

Step - 3

Hence, the radius of the circle is 5 units. But, according to the question, we need to find the diameter of the circle. We know that:

$D = 2R$

$D = 2 \times 5$

$D = 10\:units$

Final Answer

Hence, the diameter of the circle is 10 units.