What is the locus of the center of a circle?
Table of Contents
- 1 What is the locus of the center of a circle?
- 2 Which is an equation of a circle with center that passes through the point 0 0?
- 3 What is locus of Triangle?
- 4 What is the equation of a circle whose center is at the origin and the circle passes through the point 4 1 )?
- 5 What is the centre of this circle and the radius?
- 6 How many symmetrical points on a circle are centered on Y-axis?
What is the locus of the center of a circle?
A locus is a set of points that meet a given condition. The definition of a circle locus of points a given distance from a given point in a 2-dimensional plane. The given distance is the radius and the given point is the center of the circle.
Which is an equation of a circle with center that passes through the point 0 0?
The standard form equation of a circle is (x – h)2 + (y – k)2 = r2, centered at (h, k) with radius r. This circle is centered at the origin (0, 0), therefore (h, k) = (0, 0) and the equation becomes x2 + y2 = r2.
How do you find the locus of center?
- First find the centre of circles:
- Circle 1 : x^2+y^2+2x+4y+2=0.
- =>(x^2+2x+1)+(y^2+4y+4)-3=0.
- =>(x+1)^2+(y+2)^2=3.
- centre of circle is (-1,-2)
- similarly for circle 2:
- x^2+y^2+3x+3y+1=0.
- =>(x^2+2.3/2 .x+(3/2)^2)+(y^2+2.3/2*y+(3/2)^2)+1–9/2=0.
What is the equation of a circle with a center at the origin and that passes through the point 3/4 )?
Explanation: The general equation is (x−a)2+(y−b)2=r2 where (a,b) is the centre and the radius is r . The circle passes through (3,4), if we make a right angle triangle with this point and the origin.
What is locus of Triangle?
In geometry, a locus (plural: loci) (Latin word for “place”, “location”) is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
What is the equation of a circle whose center is at the origin and the circle passes through the point 4 1 )?
The equation of a circle with center (h,k) and radius r is given by (x−h)2+(y−k)2=r2 . For a circle centered at the origin, this becomes the more familiar equation x2+y2=r2 .
What is the equation of a circle whose center is at the origin and the circle passes through the point 2 5 )?
Explanation: The general equation is (x−a)2+(y−b)2=r2 where (a,b) is the centre and the radius is r .
What is the locus of the center of the circle?
What is the locus of the center of the circle which always passes through the fixed points (-a,0) and (a,0)? Let, the coordinates of the centre of the circle = (x, y). x = 0 (since a = 0). So, locus of centre of the circle is x = 0; that is, Y-axis.
What is the centre of this circle and the radius?
The centre of this circle is and the radius is The circle passes through the origin. The equation of the circle is The circle cuts the line at points and The circle passes through the origin. Let the circle be x^2+y^2–2fx-2gy=0 (constant = 0 as it passes through the origin).
How many symmetrical points on a circle are centered on Y-axis?
Since the circle is the locus of all points r distance from the center, then no set of symmetrical points about a circle centered on the y-axis can be a greater distance from the axis than r. There are points on the circle at less than r distance from the y-axis.