Advertisements
Advertisements
प्रश्न
Find the coordinates of the centre and radius of each of the following circles: x2 + y2 − ax − by = 0
Advertisements
उत्तर
The given equation can be rewritten as
∴ Centre = \[\left( \frac{a}{2}, \frac{b}{2} \right)\]
And, radius =\[\sqrt{\left( \frac{a}{2} \right)^2 + \left( \frac{b}{2} \right)^2} = \frac{1}{2}\sqrt{a^2 + b^2}\]
APPEARS IN
संबंधित प्रश्न
Find the equation of the circle with:
Centre (−2, 3) and radius 4.
Find the centre and radius of each of the following circles:
(x − 1)2 + y2 = 4
Find the centre and radius of each of the following circles:
(x + 5)2 + (y + 1)2 = 9
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 both the axes and passes through the point (2, 1).
Find the equation of a circle
passing through the origin, radius 17 and ordinate of the centre is −15.
Find the equation of the circle which touches the axes and whose centre lies on x − 2y = 3.
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 coordinates of the centre and radius of the following circle:
1/2 (x2 + y2) + x cos θ + y sin θ − 4 = 0
Find the equation of the circle passing through the points:
(5, 7), (8, 1) and (1, 3)
Show that the points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic.
Show that the points (5, 5), (6, 4), (−2, 4) and (7, 1) all lie on a circle, and find its equation, centre and radius.
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 centres of the three circles x2 + y2 − 4x − 6y − 12 = 0, x2 + y2 + 2x + 4y − 10 = 0 and x2 + y2 − 10x − 16y − 1 = 0 are collinear.
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.
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 passing through the origin and the points where the line 3x + 4y = 12 meets the axes of coordinates.
Find the equation of the circle which passes through the origin and cuts off intercepts aand b respectively from x and y - axes.
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 equation of the circle which circumscribes the triangle formed by the lines x = 0, y = 0 and lx + my = 1.
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 centroid of an equilateral triangle is (1, 1) and its one vertex is (−1, 2), then the equation of its circumcircle is
The equation of the circle passing through the origin which cuts off intercept of length 6 and 8 from the axes 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
If the circles x2 + y2 + 2ax + c = 0 and x2 + y2 + 2by + c = 0 touch each other, then
The equation of the circle circumscribing the triangle whose sides are the lines y = x + 2, 3y = 4x, 2y = 3x is ______.
Equation of the circle with centre on the y-axis and passing through the origin and the point (2, 3) is ______.
