Question

Find the length of the diameter of the circle having centre at (-3, 6) and passing through
P(1, 3)

Answer 1

$\large\text{\underline{Let's begin.}}$

$\red{\text{Diameter and Radius}}$

Diameter is the longest chord, which passes through the center of the circle. We know that the diameter is two times the length of the radius.

$\purple{\hookrightarrow\text{(Diameter)}=2\times\text{(Radius)}}$

$\red{\text{Equation of Circle}}$

The equation of a circle is $\purple{(x-a)^{2}+(y-b)^{2}=r^{2}}$, where:-

• $(a,b)$ is the center.
• $r$ is the radius.

$\red{\text{Distance Between Two Points}}$

The distance between two points is known as $\purple{\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}}$, where:-

• $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are the coordinates.

$\large\text{\underline{Solution}}$

$O(-3,6)$ and $P(1,3)$ are the coordinates which distance can be found by joining two points. One of the points $O$ is the center of the circle and $P$ is on the circle, and the distance is called the radius.

$\text{(Distance)}$

$=\sqrt{(-3-1)^{2}+(6-3)^{2}}$

$=\sqrt{4^{2}+3^{2}}$

$=\sqrt{25}$

$=5$

Since the diameter is two times the radius, the diameter is $10\text{ units}$.

$\large\text{\underline{Conclusion}}$

So, the length of the diameter is $10\text{ units}$.

$\large\text{\underline{Bonus Question}}$

Write the equation of the given circle.

$\large\text{\underline{Answer(Bonus Question)}}$

The equation of circle is $(x+3)^{2}+(y-6)^{2}=25$.

Answer 2

Given :-

Centre = (-3,6)

Point(1,3)

To Find :-

Length of diameter

Solution :-

We know that

H² = P² + B²

By using distance formula

D = √(x₁ - x₂)² + (y₁ - y₂)²

Here

• x₁ = -3
• x₂ = 1
• y₁ = 6
• y₂ = 3

D = √[(-3) - 1]² + (6 - 3)²

D = √[-4]² + (3)²

D = √16 + 9

D = √25

D = 5 cm

Now

Diameter = 2 × radius

D = 2 × 5

D = 10 cm

Hence

Diameter is 10 cm