Find the equation of a circle passing through the origin and intercepting lengths a and b on the axes.
From the figure
AD = b units and AE = a units.
D(0, b), E(a, 0) and A(0, 0) lies on the circle. C is the centre.
The general equation of a circle: (x - h)2 + (y - k)2 = r2
…(i), where (h, k) is the centre and r is the radius.
Putting A(0, 0) in (i)
(0 - h)2 + (0 - k)2 = r2
h2 + k2 = r2 …(ii)
Similarly putting D(0, b) in (i)
(0 - h)2 + (b - k)2 = r2
h2 + k2 + b2 - 2kb = r2
r2 + b2 - 2kb = r2
b2 - 2kb = 0
(b- 2k)b = 0
Either b = 0ork =
Similarly putting E(a, 0) in (i)
(a - h)2 + (0 - k)2 = r2
h2 + k2 + a2 - 2ha = r2
r2 + a2 - 2ha = r2
a2 - 2ha = 0
(a- 2h)a = 0
Either a = 0orh =
Centre = C
r2 = h2 + k2
Putting the value of r2 , h and k in equation (i)
(x - h)2 + (y - k)2 = r2
which is the required equation.
Rate this question :
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 - Mathematics
If ( - 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 - Mathematics
Find 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 - Mathematics
Find the equation of the circle concentric with the circle x2 + y2 – 6x + 12y + 15 = 0 and of double its area.RS Aggarwal - Mathematics
Find the equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4 and x + 2y = 5.RS Aggarwal - Mathematics
Show that the equation x2 + y2 + 2x + 10y + 26 = 0 represents a point circle. Also, find its centre.RS Aggarwal - Mathematics