Q. 103.7( 15 Votes )
Find the equation of the circle which passes through the points (1, 3) and (2, - 1), and has its centre on the line 2x + y – 4 = 0.
Answer :
The equation of a circle:
x2 + y2 + 2gx + 2fy + c = 0…(i)
Putting (1, 3) & (2, - 1)in (i)
2g + 6f + c = - 10..(ii)
4g - 2f + c = - 5..(iii)
Since the centre lies on the given straight line, ( - g, - f) must satisfy the equation as
- 2g –f - 4 = 0…(iv)
Solving, f = - 1, g = - 1.5, c = - 1
The equation is
x2 + y2 - 3x - 2y - 1 = 0
Rate this question :
Lecture on Common tangents & angle of intersection of 2 circles56 mins
Lecture on radical axis of 2 circles48 mins
Lecture on Tangents to a Circle57 mins
General & parametric form of circle56 mins
Family of circles55 mins
Practice Problems on Equation of Circle54 mins
Quiz on Tangents to a Circle48 mins
Interactive Quiz on radical axis of 2 circles56 mins
Interactive Quiz on Locus involving circles42 mins
Interactive Quiz on Common tangents & angle of intersection of 2 circles56 mins
Show that the quadrilateral formed by the straight lines x – y = 0, 3x + 2y = 5, x – y = 10 and 2x + 3y = 0 is cyclic and hence find the equation of the circle.
RS Aggarwal - MathematicsIf ( - 1, 3) and (∝, β) are the extremities of the diameter of the circle x2 + y2 – 6x + 5y – 7 = 0, find the coordinates (∝, β).
RS Aggarwal - MathematicsFind the equation of the circle which passes through the points A(1, 1) and B(2, 2) and whose radius is 1. Show that there are two such circles.
RS Aggarwal - MathematicsFind the equation of the circle concentric with the circle x2 + y2 – 6x + 12y + 15 = 0 and of double its area.
RS Aggarwal - MathematicsFind the equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4 and x + 2y = 5.
RS Aggarwal - MathematicsShow that the equation x2 + y2 + 2x + 10y + 26 = 0 represents a point circle. Also, find its centre.
RS Aggarwal - Mathematics