From the point P (16, 7), tangents PQ and PR are drawn to the circle x2 + y2 - 2x - 4y - 20 = 0. If C is the centre of the circle, then area of the quadrilateral PQCR is
15 sq unit
50 sq unit
75 sq unit
150 sq unit
Tangents are drawn from any point of the circle x2 + y2 = a2 to the circle x2 + y2 = b2. If the chord of contact touches the circle x2 + y2 = c2, then
a, b, c are in AP
a, b, c are in GP
a, b, c are in HP
a, b, c are in GP
The equation of tangents to the circle x2 + y2 = 4, which are parallel to x + 2y + 3 = 0, are
D.
Given equation of circle is
x2 + y2 = 4
whose centre is (0, 0) and radius is 2. The equation of line parallel to x + 2y + 3 = 0 is
...(i)
This line will be tangent to the circle, if length of perpendicular from centre = Radius of circle
On putting the value of in Eq. (i), we get
Equation of the circle, which passes through (4, 5) and whose centre is (2, 2), is
x2 + y2 + 4x + 4y - 5 = 0
x2 + y2 - 4x - 4y - 5 = 0
x2 + y2 - 4x = 13
x2 + y2 - 4x - 4y + 5 = 0
If one end of diameter of a circle x2 + y2 - 4x - 6y + 11 = 0 is (3, 4), then the other end is
(0, 0)
(1, 1)
(1, 2)
(2, 1)
Equation of the circle which passes through the points (3, - 2) and (- 2, 0) and whose centre lies on the line 2x - y - 3 = 0 , is
x2 + y2 - 3x - 12y + 2 = 0
x2 + y2 - 3x + 12y + 2 = 0
x2 + y2 + 3x + 12y + 2 = 0
x2 + y2 - 3x - 12y - 2 = 0
The end points of latusrectum of parabola x2 + 8y = 0 are
(- 4, - 2) and (4, 2)
(4, - 2) and (- 4, 2)
(- 4, - 2) and (4, - 2)
(4, 2) and (- 4, 2)
The equation of a circle passing through the vertex and the extremities of the latusrectum of the parabola y2 = 8x, is
x2 + y2 + 10x = 0
x2 + y2 + 10y = 0
x2 + y2 - 10x = 0
x2 + y2 - 5x = 0