Advertisements
Advertisements
प्रश्न
Find the centre and radius of the circle:
(x − 5)2 + (y − 3)2 = 20
Advertisements
उत्तर
Given equation of the circle is
(x − 5)2 + (y − 3)2 = 20
∴ (x − 5)2 + (y − 3)2 = `(sqrt(20))^2`
Comparing this equation with
(x − h)2 + (y − k)2 = r2, we get
h = 5, k = 3 and r = `sqrt(20) = 2sqrt(5)`
∴ Centre of the circle = (h, k) = (5, 3)
and radius of the circle = `2sqrt(5)`.
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:
`(x - 1/2)^2 + (y + 1/3)^2 = 1/36`
Find the equation of the circle with centre at (–2, 3) touching the X-axis.
Find the equation of the circle with centre at (3,1) and touching the line 8x − 15y + 25 = 0
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 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 points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic
Choose the correct alternative:
Equation of a circle which passes through (3, 6) and touches the axes is ______.
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:
If a circle passes through the point (0, 0), (a, 0) and (0, b) then find the co-ordinates of its centre
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 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.
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
Answer the following :
Find the length of the tangent segment drawn from the point (5, 3) to the circle x2 + y2 + 10x – 6y – 17 = 0
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 ______
The radius of a circle is increasing uniformly at the rate of 2.5cm/sec. The rate of increase in the area when the radius is 12cm, will be ______
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 ______.
Circle x2 + y2 – 4x = 0 touches ______.
The equation of a circle with centre at (1, 0) and circumference 10π units is ______.
