Table of Contents
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 find the coordinates of a circle with an 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.
Which point on the circle is closest to the origin?
The distance from the centre of the circle to X is 10 as it is a radius. The distance from the centre to the origin is √(−3−0)2+(−4−0)2=5. So the closest point on the circle is at a distance of 10−5=5 from the origin.
How do you find the shortest distance between two lines in 3d?
For parallel lines, the length of the line joining the two parallel lines or the length of the line perpendicular to both the parallel lines has the shortest distance. In the case of skew lines, the shortest distance is the line perpendicular to both of the given lines.
How do you find the closest point to the origin?
- (Using y-intercept form for the equation of a line, where m = slope and b is the y-intercept, we have:
- y = mx + b.
- The point on the line closest to the origin will always be the point at which a line perpendicular to the line in question passes through the origin.
- M = (-1/m)
How do you write an equation of a circle in standard form?
The standard form of a circle’s equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius. To convert an equation to standard form, you can always complete the square separately in x and y.
How do you find the equation of a circle with center?
The equation of circle with (h,k) center and r radius is given by: (x-h) 2 + (y-k) 2 = r 2. Thus, if we know the coordinates of the center of the circle and its radius as well, we can easily find its equation. Example: Say point (1,2) is the center of the circle and radius is equal to 4
What is the formula to find the radius of a circle?
Therefore, the radius of a circle is CP. By using distance formula, (x-h) 2 + (y-k) 2 = CP 2. Let radius be ‘a’. Therefore, the equation of the circle with centre (h, k) and the radius ‘ a’ is, (x-h) 2 +(y-k) 2 = a 2. which is called the standard form for the equation of a circle. Equation of a Circle in General Form
What is the center radius of a circle with radius 7?
When the center point is the origin (0, 0) of the graph, the center-radius form is greatly simplified: x2 + y2 = r2 For example, a circle with a radius of 7 units and a center at (0, 0) looks like this as a formula and a graph: x 2 + y 2 = 49
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.