Advertisements
Advertisements
प्रश्न
If the equation of a circle is λx2 + (2λ − 3) y2 − 4x + 6y − 1 = 0, then the coordinates of centre are
पर्याय
(4/3, −1)
(2/3, −1)
(−2/3, 1)
(2/3, 1)
उत्तर
(2/3, −1)
To find the centre:
Coefficient of x2 = Coefficient of y2
\[\therefore \lambda = 2\lambda - 3 \Rightarrow \lambda = 3\]
Therefore, the given equation can be rewritten as
APPEARS IN
संबंधित प्रश्न
Find the equation of the circle with:
Centre (−2, 3) and radius 4.
Find the equation of the circle with:
Centre (a cos α, a sin α) and radius a.
Find the equation of the circle with:
Centre (a, a) and radius \[\sqrt{2}\]a.
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 x-axis at a distance 5 from the origin and radius 6 units.
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.
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.
Find the coordinates of the centre and radius of each of the following circles: 2x2 + 2y2 − 3x + 5y = 7
Find the coordinates of the centre and radius of each of the following circles: x2 + y2 − ax − by = 0
Find the equation of the circle passing through the points:
(5, 7), (8, 1) and (1, 3)
Find the equation of the circle passing through the points:
(0, 0), (−2, 1) and (−3, 2)
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 2x + y − 3 = 0, x + y − 1 = 0 and 3x + 2y − 5 = 0
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.
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.
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 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 which passes through the origin and cuts off intercepts aand b respectively from x and y - axes.
Write the length of the intercept made by the circle x2 + y2 + 2x − 4y − 5 = 0 on y-axis.
Write the coordinates of the centre of the circle passing through (0, 0), (4, 0) and (0, −6).
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 2x2 + λxy + 2y2 + (λ − 4) x + 6y − 5 = 0 is the equation of a circle, then its radius 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
The equation of the incircle formed by the coordinate axes and the line 4x + 3y = 6 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 a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is ______.