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 (0, −1) and radius 1.
Find the equation of the circle with:
Centre (a, a) and radius \[\sqrt{2}\]a.
Find the centre and radius of each of the following circles:
(x + 5)2 + (y + 1)2 = 9
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.
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.
Find the equations of the circles touching y-axis at (0, 3) and making an intercept of 8 units on the X-axis.
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 + 6x − 8y − 24 = 0
Find the equation of the circle which passes through (3, −2), (−2, 0) and has its centre on the line 2x − y = 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 concentric with the circle x2 + y2 − 6x + 12y + 15 = 0 and double of its area.
Find the equation of the circle concentric with x2 + y2 − 4x − 6y − 3 = 0 and which touches the y-axis.
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.
The abscissae of the two points A and B are the roots of the equation x2 + 2ax − b2 = 0 and their ordinates are the roots of the equation x2 + 2px − q2 = 0. Find the equation of the circle with AB as diameter. Also, find its radius.
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.
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.
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.
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
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 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 circle passing through the point (1, 1) and having two diameters along the pair of lines x2 − y2 −2x + 4y − 3 = 0, 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 =
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 ______.
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 ______.
