PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions

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

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

Prove that:

Prove that:

Prove that: 

Show that :

Show that :

Prove that:
cos 10° cos 30° cos 50° cos 70° = \[\frac{3}{16}\]