Advertisements
Advertisements
Question
Find the centre and radius of each of the following circles:
(x + 5)2 + (y + 1)2 = 9
Advertisements
Solution
Let (h, k) be the centre of a circle with radius a.
Thus, its equation will be
\[\left( x - h \right)^2 + \left( y - k \right)^2 = a^2\]
Given:
(x + 5)2 + (y + 1)2 = 9
Here, h = −5, k = −1 and radius = 3
Thus, the centre is (−5, −1) and the radius is 3.
APPEARS IN
RELATED QUESTIONS
Find the equation of the circle with:
Centre (a, b) and radius\[\sqrt{a^2 + b^2}\]
Find the equation of the circle passing through the point of intersection of the lines x + 3y = 0 and 2x − 7y = 0 and whose centre is the point of intersection of the lines x + y + 1 = 0 and x − 2y + 4 = 0.
Find the equation of the circle whose centre lies on the positive direction of y - axis at a distance 6 from the origin and whose radius is 4.
If the equations of two diameters of a circle are 2x + y = 6 and 3x + 2y = 4 and the radius is 10, find the equation of the circle.
A circle of radius 4 units touches the coordinate axes in the first quadrant. Find the equations of its images with respect to the line mirrors x = 0 and y = 0.
Find the equations of the circles touching y-axis at (0, 3) and making an intercept of 8 units on the X-axis.
If the lines 2x − 3y = 5 and 3x − 4y = 7 are the diameters of a circle of area 154 square units, then obtain the equation of the circle.
If the line y = \[\sqrt{3}\] x + k touches the circle x2 + y2 = 16, then find the value of k.
Show that the point (x, y) given by \[x = \frac{2at}{1 + t^2}\] and \[y = a\left( \frac{1 - t^2}{1 + t^2} \right)\] lies on a circle for all real values of t such that \[- 1 \leq t \leq 1\] where a is any given real number.
Find the coordinates of the centre and radius of each of the following circles: x2 + y2 + 6x − 8y − 24 = 0
Find the coordinates of the centre and radius of the following circle:
1/2 (x2 + y2) + x cos θ + y sin θ − 4 = 0
Show that the points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic.
Find the equation of the circle which circumscribes the triangle formed by the lines 2x + y − 3 = 0, x + y − 1 = 0 and 3x + 2y − 5 = 0
If a circle passes through the point (0, 0),(a, 0),(0, b) then find the coordinates of its centre.
Find the equation of the circle, the end points of whose diameter are (2, −3) and (−2, 4). Find its centre and radius.
Find the equation of the circle passing through the origin and the points where the line 3x + 4y = 12 meets the axes of coordinates.
Write the length of the intercept made by the circle x2 + y2 + 2x − 4y − 5 = 0 on y-axis.
If the abscissae and ordinates of two points P and Q are roots of the equations x2 + 2ax − b2 = 0 and x2 + 2px − q2 = 0 respectively, then write the equation of the circle with PQ as diameter.
Write the equation of the unit circle concentric with x2 + y2 − 8x + 4y − 8 = 0.
Write the area of the circle passing through (−2, 6) and having its centre at (1, 2).
If 2x2 + λxy + 2y2 + (λ − 4) x + 6y − 5 = 0 is the equation of a circle, then its radius is
The equation x2 + y2 + 2x − 4y + 5 = 0 represents
The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines x2 − y2 −2x + 4y − 3 = 0, is
If the point (λ, λ + 1) lies inside the region bounded by the curve \[x = \sqrt{25 - y^2}\] and y-axis, then λ belongs to the interval
The equation of a circle with radius 5 and touching both the coordinate axes is
The equation of the circle passing through the origin which cuts off intercept of length 6 and 8 from the axes is
The equation of the circle concentric with x2 + y2 − 3x + 4y − c = 0 and passing through (−1, −2) is
The equation of the circle which touches the axes of coordinates and the line \[\frac{x}{3} + \frac{y}{4} = 1\] and whose centres lie in the first quadrant is x2 + y2 − 2cx − 2cy + c2 = 0, where c is equal to
If the circles x2 + y2 = a and x2 + y2 − 6x − 8y + 9 = 0, touch externally, then a =
If (x, 3) and (3, 5) are the extremities of a diameter of a circle with centre at (2, y), then the values of x and y are
If (−3, 2) lies on the circle x2 + y2 + 2gx + 2fy + c = 0 which is concentric with the circle x2 + y2 + 6x + 8y − 5 = 0, then c =
The equation of the circle circumscribing the triangle whose sides are the lines y = x + 2, 3y = 4x, 2y = 3x is ______.
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 ______.
