Advertisements
Advertisements
Question
The radius of the circle represented by the equation 3x2 + 3y2 + λxy + 9x + (λ − 6) y + 3 = 0 is
Options
\[\frac{3}{2}\]
\[\frac{\sqrt{17}}{2}\]
2/3
none of these
Advertisements
Solution
\[\frac{3}{2}\]
The equation of the circle is 3x2 + 3y2 + λxy + 9x + (λ − 6) y + 3 = 0.
∴ Coefficient of xy = 0
\[\Rightarrow \lambda = 0\]
\[\therefore 3 x^2 + 3 y^2 + 9x - 6y + 3 = 0\]
\[ \Rightarrow x^2 + y^2 + 3x - 2y + 1 = 0\]
Therefore, the radius of the circle is
APPEARS IN
RELATED QUESTIONS
Find the equation of the circle with:
Centre (−2, 3) and radius 4.
Find the equation of the circle with:
Centre (a, b) and radius\[\sqrt{a^2 + b^2}\]
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.
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.
If the line y = \[\sqrt{3}\] x + k touches the circle x2 + y2 = 16, then find the value of k.
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 coordinates of the centre and radius of each of the following circles: 2x2 + 2y2 − 3x + 5y = 7
Find the equation of the circle which circumscribes the triangle formed by the lines
x + y = 2, 3x − 4y = 6 and x − y = 0.
Find the equation of the circle which circumscribes the triangle formed by the lines y = x + 2, 3y = 4x and 2y = 3x.
Find the equation of the circle concentric with x2 + y2 − 4x − 6y − 3 = 0 and which touches the y-axis.
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 which passes through the points (2, 3) and (4,5) and the centre lies on the straight line y − 4x + 3 = 0.
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.
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.
Write the length of the intercept made by the circle x2 + y2 + 2x − 4y − 5 = 0 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.
Write the area of the circle passing through (−2, 6) and having its centre at (1, 2).
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
If the centroid of an equilateral triangle is (1, 1) and its one vertex is (−1, 2), then the equation of its circumcircle 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
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
The equation of a circle with radius 5 and touching both the coordinate axes is
The equation of the circle concentric with x2 + y2 − 3x + 4y − c = 0 and passing through (−1, −2) is
The area of an equilateral triangle inscribed in the circle x2 + y2 − 6x − 8y − 25 = 0 is
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
Equation of a circle which passes through (3, 6) and touches the axes is ______.
