Advertisements
Advertisements
प्रश्न
Find the equation of the circle which circumscribes the triangle formed by the lines
x + y = 2, 3x − 4y = 6 and x − y = 0.
Advertisements
उत्तर
In \[∆\]ABC:
Let AB represent the line x + y = 2. ...(1)
Let BC represent the line 3x − 4y = 6. ...(2)
Let CA represent the line x − y = 0. ...(3)
Intersection point of (1) and (3) is (1, 1).
Intersection point of (1) and (2) is (2, 0).
Intersection point of (2) and (3) is (−6, −6).
The coordinates of A, B and C are (1, 1), (2, 0) and (−6, −6), respectively.
Let the equation of the circumcircle be
It passes through A, B and C.
∴ \[2 + 2g + 2f + c = 0\]
Hence, the required equation of the circumcircle is
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 + 5)2 + (y + 1)2 = 9
Find the centre and radius of each of the following circles:
x2 + y2 − 4x + 6y = 5
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.
Find the equation of the circle which touches the axes and whose centre lies on x − 2y = 3.
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.
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 lines 3x − 4y + 4 = 0 and 6x − 8y − 7 = 0 are tangents to a circle, then find the radius of the circle.
If the line 2x − y + 1 = 0 touches the circle at the point (2, 5) and the centre of the circle lies on the line x + y − 9 = 0. Find the equation of the circle.
Find the equation of the circle passing through the points:
(5, −8), (−2, 9) and (2, 1)
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 x + y + 3 = 0, x − y + 1 = 0 and x = 3
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 which passes through the origin and cuts off chords of lengths 4 and 6 on the positive side of the x-axis and y-axis respectively.
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.
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 whose diameter is the line segment joining (−4, 3) and (12, −1). Find also the intercept made by it 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.
If 2x2 + λxy + 2y2 + (λ − 4) x + 6y − 5 = 0 is the equation of a circle, then its radius 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
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
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 ______.
Equation of the circle with centre on the y-axis and passing through the origin and the point (2, 3) 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 ______.
