Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:
ABCD is a square with side a units.
Let AB and AD represent the x-axis and the y-axis, respectively.
Thus, the coordinates of B and D are (a, 0) and (0, a), respectively.
The end points of the diameter of the circle circumscribing the square are B and D.
Thus, equation of the circle circumscribing the square is
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:
x2 + y2 − 4x + 6y = 5
Find the centre and radius of each of the following circles:
x2 + y2 − x + 2y − 3 = 0.
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 a circle
passing through the origin, radius 17 and ordinate of the centre is −15.
Find the equation of the circle which has its centre at the point (3, 4) and touches the straight line 5x + 12y − 1 = 0.
A circle whose centre is the point of intersection of the lines 2x − 3y + 4 = 0 and 3x + 4y− 5 = 0 passes through the origin. Find its equation.
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.
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 each of the following circles: x2 + y2 − ax − by = 0
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 concentric with the circle x2 + y2 − 6x + 12y + 15 = 0 and double of its area.
Find the equation to the circle which passes through the points (1, 1) (2, 2) and whose radius is 1. Show that there are two such circles.
Find the equation of the circle, the end points of whose diameter are (2, −3) and (−2, 4). Find its centre and radius.
The sides of a square are x = 6, x = 9, y = 3 and y = 6. Find the equation of a circle drawn on the diagonal of the square as its diameter.
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 passing through the origin and the points where the line 3x + 4y = 12 meets the axes of coordinates.
The line 2x − y + 6 = 0 meets the circle x2 + y2 − 2y − 9 = 0 at A and B. Find the equation of the circle on AB as diameter.
Find the equation of the circle which circumscribes the triangle formed by the lines x = 0, y = 0 and lx + my = 1.
Write the equation of the unit circle concentric with x2 + y2 − 8x + 4y − 8 = 0.
If the radius of the circle x2 + y2 + ax + (1 − a) y + 5 = 0 does not exceed 5, write the number of integral values a.
If the equation of a circle is λx2 + (2λ − 3) y2 − 4x + 6y − 1 = 0, then the coordinates of centre are
The radius of the circle represented by the equation 3x2 + 3y2 + λxy + 9x + (λ − 6) y + 3 = 0 is
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 the incircle formed by the coordinate axes and the line 4x + 3y = 6 is
The equation of a circle with radius 5 and touching both the coordinate axes is
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
Equation of a circle which passes through (3, 6) and touches the axes 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 ______.
