Question

A circle touches the x-axis and also touches the circle with centre (0, 3) and radius 2. The locus of the centre of the circle is:

Solution

Correct option is

Parabola 

Let the circle be (hk), k as it touches the axis of x. Again it touches the circle (0, 3), 2 therefore distance between the centres is equal to r1 ± r2

  

         

or x2 = 2y – 5

In either case it is a parabola.

SIMILAR QUESTIONS

Q1

1:- The chords in which the circle C cuts the members of the family S of circles through A and B are con-current at  

Q2

2:- Equations of the member of the family S which bisects the circumference of C is

Q3

3:- If O is the origin and P is the centre of C, then the difference of the squares of the lengths of the tangents from A and B to the circle is equal to

Q4

If the two (x – 1)2 + (y – 3)2 = r2 and x2 + y2 – 8x + 2y + 8 = 0 intersect in two distinct points, then

Q5

The distance between the chords of contact of the tangent to the circle x2 + y2 + 2gx + 2fy + c = 0 from the origin and the point (gf) is

Q6

The angle between the tangents drawn from the origin to the circle (x – 7)2 + (y + 1)2 = 25 is

Q7

A square is inscribed in the circle x2 + y2 – 2x + 4y + 3 = 0. Its sides are parallel to the co-ordinates axes. Then one vertex of the square is

Q8

If the lines 3x – 4y – 7 = 0 and 2x – 3y – 5 = 0 are two diameters of a circle of area 49π square units, then the equation of the circle is:

Q9

A variable circle passes through a fixed point A(pq) and touches the x-axis. The locus of the other end of the diameter through A is:

Q10

The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have co-ordinates (3, 4) and (–4, 3) respectively than QPR is equal  to