Advertisements
Advertisements
प्रश्न
Answer the following :
Find the equation of the circle concentric with x2 + y2 – 4x + 6y = 1 and having radius 4 units
Advertisements
उत्तर
Given equation of circle is
x2 + y2 – 4x + 6y = 1
i.e., x2 + y2 – 4x + 6y – 1 = 0
Comparing this equation with
x2 + y2 + 2gx + 2fy + c = 0, we get
2g = –4, 2f = 6
∴ g = –2, f = 3
∴ Centre of the circle = (–g, –f) = (2, –3)
Given circle is concentric with the required circle.
∴ They have same centre.
∴ Centre of the required circle = (2, –3)
The equation of a circle with centre at (h, k) and radius r is
(x – h)2 + (y – k)2 = r2
Here, h = 2, k = –3 and r = 4
∴ the required equation of the circle is
(x – 2)2 + [y – (–3)]2 = 42
∴ (x – 2)2 + (y + 3)2 = 16
∴ x2 – 4x + 4 + y2 + 6y + 9 – 16 = 0
∴ x2 + y2 – 4x + 6y – 3 = 0.
APPEARS IN
संबंधित प्रश्न
Find the equation of the circle with centre at (2, −3) and radius 5.
Find the equation of the circle with centre at (−3, −3) passing through the point (−3, −6)
Find the centre and radius of the circle:
x2 + y2 = 25
Find the centre and radius of the circle:
(x − 5)2 + (y − 3)2 = 20
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 at (–2, 3) touching the X-axis.
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 centre and radius of the following:
x2 + y2 − 2x + 4y − 4 = 0
Find the centre and radius of the following:
x2 + y2 − 6x − 8y − 24 = 0
Find the centre and radius of the following:
4x2 + 4y2 − 24x − 8y − 24 = 0
Show that the equation 3x2 + 3y2 + 12x + 18y − 11 = 0 represents a circle
Choose the correct alternative:
Equation of a circle which passes through (3, 6) and touches the axes is ______.
Choose the correct alternative:
If the lines 2x − 3y = 5 and 3x − 4y = 7 are the diameters of a circle of area 154 sq. units, then find the equation of the circle
Choose the correct alternative:
Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y − 4x + 3 = 0
Choose the correct alternative:
If the lines 3x − 4y + 4 = 0 and 6x − 8y − 7 = 0 are tangents to a circle, then find the radius of the circle
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
Answer the following :
Show that the points (9, 1), (7, 9), (−2, 12) and (6, 10) are concyclic
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 :
Show that the circles touch each other externally. Find their point of contact and the equation of their common tangent:
x2 + y2 – 4x + 10y +20 = 0,
x2 + y2 + 8x – 6y – 24 = 0.
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 ______
The centre of the circle x = 3 + 5 cos θ, y = - 4 + 5 sin θ, 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 ______
If x2 + (2h - 1)xy + y2 - 24x - 8y + k = 0 is the equation of the circle and 12 is the radius of the circle, then ______.
The equation of circle whose diameter is the line joining the points (–5, 3) and (13, –3) is ______.
Let AB be a chord of the circle x2 + y2 = r2 subtending a right angle at the centre, then the locus of the centroid of the ΔPAB as P moves on the circle is ______.
