Learn the general equation of a circle when the center is at origin and when it is not in origin. Circle equation can be derived using Pythagoras theorem as well. Solve questions at BYJU’S.
For example: 1. Find the equation of this circle: The center point is not marked on this circle, but we can find it fairly easily: So from this we can tell that our center point is (2, -3) and the radius is 4. (To find the radius, simply count the number of spaces from the ...
centreattheorigin(O)ofradius1unit. x y O ByPythagoras’Theoremweseethatx 2 +y 2 =1 Thismeansthatallpointsonthe circumferenceofthiscircleare satisfiedbyitsequation. Soforexampleconsiderthe points(1,0)and(0,1)inturn. 1 2 +0 2 =10
Unit Circle Examples Example 1: Does the point P (1/2, 1/2) lie on the unit circle? Solution: We know that equation of a unit circle is: x2 + y2 = 1 Substituting x = 1/2 and y = 1/2, we get: = x2 + y2 = (1/2)2 + (1/2)2 = 1/4 + 1/4 = 1/2 ≠ 1 ...
Consider a circle with center-radius equation (x−1)2+(y+2)2=9. Developing the left-hand side of the equation gives x2−2x+1+y2+4y+4=9⟹x2+y2−2x+4y−4=0, which is the standard equation of the given circle. Consider now a new example. Let x2+y2+4x−6y−12...
百度试题 结果1 题目 Example 15: Find the equation of the circle whose center is on y= - 2x. The line x +y =1 is tangent to the circle at(2, -1). 相关知识点: 试题来源: 解析 优质解答 反馈 收藏
circle, standard equation of The equation(x-h)2+(y-k)^2=r^2r epresents a circle of radius r and center at the point(h, k). For example, the equatio n(x-5)^2+(y+3)^2=16 represents a circle with radius 4 and center at (5,-3). If h=k=0 and r=1, we get the e...
General Equation of a Circle Definition A circle is defined as the locus of a point that moves in a plane such that its distance from a fixed point in that plane is always constant. The fixed point is called the centre of the circle and the constant distance is called the radius of the...
For example, a circle centered at (a,b) and radius r is given as (x−a)2+(y−b)2=r2.Sometimes, we need to complete the square to bring the equation of a conic to the standard form to determine the important features of the curve. ...
An expression is a combination of digits, variables, and mathematical operations. πr2 2L+2W 3x Equations are two expressions that are equal to each other. Area of a circle: A=πr2 Perimeter of a rectangle: P=2L+2W Linear equation: 3x=7x+5 Characteristics of Equations Must...