How do you find the equation of the circle when given two points on the circle?

The equation of a circle with center (h,k) and radius r units is (x−h)2+(y−k)2=r2 .

How do you find the x and y coordinates of a circle?

Typically, to find the x, y coordinates on a circle with a known radius and angle you could simply use the formula x = r(cos(degrees‎°)), y = r(sin(degrees‎°)). The circle would look like this and the degrees would expand counterclockwise from 0‎°.

How do you solve a circle equation?

The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. If a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.

What do you call the line that touches the circle at exactly one point?

A tangent to a circle is a straight line which touches the circle at only one point. This point is called the point of tangency. The tangent to a circle is perpendicular to the radius at the point of tangency.

How to find the general equation of a circle with two points?

If the given circle is passing through two points, say A (x 1, y 1) and B (x 2, y 2), then these points must satisfy the general equation of a circle. Now put these two points in the given equation of a circle, i.e.: x 1 2 + y 1 2 + 2 g x 1 + 2 f y 1 + c = 0 – – – (i) x 2 2 + y 2 2 + 2 g x 2 + 2 f y 2 + c = 0 – – – (ii)

What is the equation of circle with (H) K and (r) radius?

A circle is a closed curve that is drawn from the fixed point called the centre, in which all the points on the curve are having the same distance from the centre point of the centre. The equation of circle with (h,k) center and r radius is given by: (x-h) 2 + (y-k) 2 = r 2

How do you find the coordinates of the center of a circle?

If two points on the circle are given as (x1,y1) and (x2,y2) along with radius as r, simply substitute the values in the general equation and solve for g & h. We get values of (g,h) ,i.e, the coordinates of centre of circle.

What is the condition for the equation to represent a circle?

However, the condition for the equation to represent a circle is \\(a = b\\) and \\(h = 0\\). Unfortunately, it can be difficult to decipher any meaningful properties about a given circle from its general equation, so completing the square allows quick conversion to the standard form, which contains values for the center and radius of the circle.