Question

Determine the equation of the circle with centre (-3;5) and passing through a point (2;-9)

Answer 1

Therefore, the equation of circle is: $(x+3)^{2}+(y+5)^{2} = 100$

What is a circle?

• All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
• The radius of a circle is the separation between any point on the circle and its center.
• The radius must typically be a positive integer. Except when otherwise specified, this article discusses circles in Euclidean geometry, namely the Euclidean plane.
• A circle, specifically, is a straightforward closed curve that separates the plane into its inner and exterior.

Here we know that$(h,k) = (-3,5)$but we are not given the radius.

However, we can find the radius by using the distance formula.

$\sqrt{x^{2} +y^{2} }$, where $x=x_{1} -x_{2}$ and $y=y_{1} -y_{2}$

Putting the values, we get:

$\sqrt{8^{2} +6^{2} }$

The radius comes out to be:

$r=10$

An equation of the circle with center $(h,k)$ and radius r is

$(x-h)^{2} +(y-k)^{2} = r^{2}$

Now, substituting the values, we get:

$(x--3)^{2} +(y-5)^{2} = 10^{2}$

Therefore, the equation of circle is:

$(x+3)^{2}+(y+5)^{2} = 100$

Know more about circles with the help of the given link:

brainly.com/question/10618691

#SPJ4