Advertisements
Advertisements
Question
Find the equation of a circle with radius 4 units and touching both the co-ordinate axes having centre in third quadrant.
Advertisements
Solution
Radius of the circle = 4 units
Since the circle touches both the co-ordinate axes and its centre is in third quadrant,
the centre of the circle is C (– 4, – 4).
The equation of a circle with centre at (h, k) and radius r is given by
(x – h)2 + (y – k)2 = r2
Here, h = – 4, k = – 4, r = 4
∴ the required equation of the circle is
[x – (– 4)]2 + [y – (– 4)]2 = 42
∴ (x + 4)2 + (y + 4)2 = 16
∴ x2 + 8x + 16 + y2 + 8y + 16 – 16 = 0
∴ x2 + y2 + 8x + 8y + 16 = 0.
APPEARS IN
RELATED QUESTIONS
Find the equation of the circle with centre at origin and radius 4.
Find the equation of the circle with centre at (−3, −2) and radius 6.
Find the equation of the circle with centre at (2, −3) and radius 5.
Find the centre and radius of the circle:
x2 + y2 = 25
Find the centre and radius of the circle:
`(x - 1/2)^2 + (y + 1/3)^2 = 1/36`
Find the equation of the circle with centre at (a, b) touching the Y-axis
Find the equation of the circle with centre on the X-axis and passing through the origin having radius 4.
Find the equation of the circle with centre at (3,1) and touching the line 8x − 15y + 25 = 0
Find the equation circle if the equations of two diameters are 2x + y = 6 and 3x + 2y = 4. When radius of circle is 9
If y = 2x is a chord of circle x2 + y2−10x = 0, find the equation of circle with this chord as diametre
Find the equation of circle (a) passing through the origin and having intercepts 4 and −5 on the co-ordinate axes
Find the equation of a circle passing through the points (1,−4), (5,2) and having its centre on the line x − 2y + 9 = 0
Find the equation of the circle passing through the points (5, 7), (6, 6) and (2, −2)
Choose the correct alternative:
Area of the circle centre at (1, 2) and passing through (4, 6) is
Choose the correct alternative:
The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is
Answer the following :
Find the centre and radius of the circle x2 + y2 − x +2y − 3 = 0
Answer the following :
Find the centre and radius of the circle x = 3 – 4 sinθ, y = 2 – 4cosθ
Answer the following :
Find the equation of circle passing through the point of intersection of the lines x + 3y = 0 and 2x − 7y = 0 whose centre is the point of intersection of lines x + y + 1 = 0 and x − 2y + 4 = 0
The line 2x − y + 6 = 0 meets the circle x2 + y2 + 10x + 9 = 0 at A and B. Find the equation of circle on AB as diameter.
Answer the following :
Find the equation of the circle concentric with x2 + y2 – 4x + 6y = 1 and having radius 4 units
Answer the following :
Show that the circles touch each other externally. Find their point of contact and the equation of their common tangent:
x2 + y2 – 4x – 10y + 19 = 0,
x2 + y2 + 2x + 8y – 23 = 0.
Answer the following :
Show that the circles touch each other internally. Find their point of contact and the equation of their common tangent:
x2 + y2 + 4x – 12y + 4 = 0,
x2 + y2 – 2x – 4y + 4 = 0
If 2x - 4y = 9 and 6x - 12y + 7 = 0 are the tangents of same circle, then its radius will be ______
If one of the diameters of the curve x2 + y2 - 4x - 6y + 9 = 0 is a chord of a circle with centre (1, 1), then the radius of this circle is ______
If the radius of a circle increases from 3 cm to 3.2 cm, then the increase in the area of the circle is ______
The equation of the circle with centre (4, 5) which passes through (7, 3) is ______.
The equation of circle whose diameter is the line joining the points (–5, 3) and (13, –3) is ______.
The equation of a circle with centre at (1, 0) and circumference 10π units is ______.
