PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Mathematics

If the equation (4a − 3) x2 + ay2 + 6x − 2y + 2 = 0 represents a circle, then its centre is ______. 

The radius of the circle represented by the equation 3x² + 3y² + λxy + 9x + (λ − 6) y + 3 = 0 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 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

If the circles x² + y² = 9 and x² + y² + 8y + c = 0 touch each other, then c is equal to

If the circle x² + y² + 2ax + 8y + 16 = 0 touches x-axis, then the value of a 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

The circle x² + y² + 2gx + 2fy + c = 0 does not intersect x-axis, if

The area of an equilateral triangle inscribed in the circle x² + y² − 6x − 8y − 25 = 0 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