Advertisements
Advertisements
प्रश्न
Find the centre and radius of each of the following circles:
(x + 5)2 + (y + 1)2 = 9
उत्तर
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
संबंधित प्रश्न
Find the equation of the circle with:
Centre (a, b) and radius\[\sqrt{a^2 + b^2}\]
Find the equation of the circle with:
Centre (0, −1) and radius 1.
Find the centre and radius of each of the following circles:
(x − 1)2 + y2 = 4
Find the equation of the circle whose centre is (1, 2) and which passes through the point (4, 6).
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.
Find the equation of a circle which touches x-axis at a distance 5 from the origin and radius 6 units.
Find the equation of the circle which touches the axes and whose centre lies on x − 2y = 3.
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.
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.
Find the equation of the circle having (1, −2) as its centre and passing through the intersection of the lines 3x + y = 14 and 2x + 5y = 18.
One diameter of the circle circumscribing the rectangle ABCD is 4y = x + 7. If the coordinates of A and B are (−3, 4) and (5, 4) respectively, find the equation of the circle.
Find the equation of the circle passing through the points:
(5, 7), (8, 1) and (1, 3)
Find the equation of the circle which circumscribes the triangle formed by the lines x + y + 3 = 0, x − y + 1 = 0 and x = 3
Find the equation of the circle which circumscribes the triangle formed by the lines
x + y = 2, 3x − 4y = 6 and x − y = 0.
Find the equation of the circle which circumscribes the triangle formed by the lines y = x + 2, 3y = 4x and 2y = 3x.
Prove that the radii of the circles x2 + y2 = 1, x2 + y2 − 2x − 6y − 6 = 0 and x2 + y2 − 4x − 12y − 9 = 0 are in A.P.
Find the equation of the circle concentric with the circle x2 + y2 − 6x + 12y + 15 = 0 and double of its area.
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 the end points of whose diameter are the centres of the circles x2 + y2 + 6x − 14y − 1 = 0 and x2 + y2 − 4x + 10y − 2 = 0.
Find the equation of the circle circumscribing the rectangle whose sides are x − 3y = 4, 3x + y = 22, x − 3y = 14 and 3x + y = 62.
Find the equation of the circle which passes through the origin and cuts off intercepts aand b respectively from x and y - axes.
Find the equation of the circle whose diameter is the line segment joining (−4, 3) and (12, −1). Find also the intercept made by it on y-axis.
ABCD is a square whose side is a; taking AB and AD as axes, prove that the equation of the circle circumscribing the square is x2 + y2 − a (x + y) = 0.
Find the equations of the circles which pass through the origin and cut off equal chords of \[\sqrt{2}\] units from the lines y = x and y = − x.
Write the coordinates of the centre of the circle passing through (0, 0), (4, 0) and (0, −6).
Write the area of the circle passing through (−2, 6) and having its centre at (1, 2).
The number of integral values of λ for which the equation x2 + y2 + λx + (1 − λ) y + 5 = 0 is the equation of a circle whose radius cannot exceed 5, is
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
Equation of the diameter of the circle x2 + y2 − 2x + 4y = 0 which passes through the origin is
Equation of the circle through origin which cuts intercepts of length a and b on axes is
Equation of a circle which passes through (3, 6) and touches the axes is ______.
