Advertisements
Advertisements
प्रश्न
Show that the points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic.
उत्तर
Let the required equation of the circle be
Hence, the points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic.
APPEARS IN
संबंधित प्रश्न
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.
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 a circle
which touches both the axes at a distance of 6 units from the origin.
Find the equation of a circle
which touches both the axes and passes through the point (2, 1).
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.
Show that the point (x, y) given by \[x = \frac{2at}{1 + t^2}\] and \[y = a\left( \frac{1 - t^2}{1 + t^2} \right)\] lies on a circle for all real values of t such that \[- 1 \leq t \leq 1\] where a is any given real number.
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.
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 (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 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 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 whose diameter is the line segment joining (−4, 3) and (12, −1). Find also the intercept made by it on y-axis.
Write the length of the intercept made by the circle x2 + y2 + 2x − 4y − 5 = 0 on y-axis.
If the equation of a circle is λx2 + (2λ − 3) y2 − 4x + 6y − 1 = 0, then the coordinates of centre are
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 point (2, k) lies outside the circles x2 + y2 + x − 2y − 14 = 0 and x2 + y2 = 13 then k lies in the interval
If the point (λ, λ + 1) lies inside the region bounded by the curve \[x = \sqrt{25 - y^2}\] and y-axis, then λ belongs to the interval
If the circles x2 + y2 = 9 and x2 + y2 + 8y + c = 0 touch each other, then c is equal to
The equation of the circle concentric with x2 + y2 − 3x + 4y − c = 0 and passing through (−1, −2) is
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 =
The equation of the circle circumscribing the triangle whose sides are the lines y = x + 2, 3y = 4x, 2y = 3x is ______.
Equation of a circle which passes through (3, 6) and touches the axes 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 ______.
