The set of lines  where  is concurrent at the point . . .

If a, b, c are in Arithmetic Progression then the straight line
 will pass through a fixed point whose coordinates are  . . . . .

Given the points A (0, 4) and B (0, - 4) the equation of the locus of the point P (x, y) such that |AP – BP| = 6 is . . . . .

If the algebraic sum of the perpendicular distance from the point
(2, 0), (0, 2) and (1, 1) to a variable straight line be zero then the line passes through a fixed point whose coordinates are

Two circles  and  are given. Then the equation of the circle through their points of intersection and the point (1, 1) is

a)

b)

c)

d) None of these

The equation of the circles through (1, 1) and the point of intersection of
 
is

a)

b)

c)

d) None of these

If a circle passes through the points (a, b) and cuts the circle  orthogonally, then the equation of the locus of its centre is

a)

b)

c)

d)

If two circles  and  intersect in two distinct points, then

a) 2 < r < 8

b) r < 2

c) r = 2

d) r > 2

The lines  and  are diameters of a circle of area 154 square units. Then the equation of the circle is

a)

b)

c)

d)

Find the centre of the circle passing through (0, 0) and (1, 0) and touching the circle .

The locus of the centre of circles which touches externally  and which touches the Y-axis is given by the equation

a)

b)

c)

d)

The angle between a pair of tangents drawn from a point P to the circle  is 2α. Then the locus of P is

a)

b)

c)

d)

The number of common tangents to the circles  and  is

a) 0

b) 1

c) 3

d) 4

If two distinct chords drawn from the point (p, q) on the circle  (where pq ≠ 0) are bisected by the X-axis then

a)

b)

c)

d)

The triangle PQR is inscribed in the circle. If Q and R  have coordinates (3, 4) and (-4, 3) respectively, then the ∠QPR is equal to

a)

b)

c)

d)

If the circles  and  intersect orthogonally then k is

a) 2 or

b) – 2  or

c) 2 or

d) – 2 or

If the tangent at the point P on the circle  meets the straight line  at a point Q on the Y-axis, then the length of PˆQ is

a) 4

b)

c) 5

d)

If a > 2b > 0 then the positive value of m for which
 is a common tangent to  and is

a)

b)

c)

d)

The centre of the circle inscribed in the square formed by the lines  and

a) (4, 7)

b) (7, 4)

c) (9, 4)

d) (4, 9)

If one of the diameters of the circle  is a chord to the circle with centre (2, 1) then the radius of the circle is

a)

b)

c) 3

d) 2

A circle is given by , another circle C touches it externally and also the X-axis, then the locus of the centre of C is

a)

b)

c)

d)

Tangent to the curve  at the point P(1, 7) touches the circle  at a point Q then the coordinates of Q are

a)

b)

c)

d)

The equation of the tangents drawn from the origin to the circle  are

a) x= 6

b) y = 0

c)

d)