Question

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:

Solution

Correct option is

(x – p)2 = 4qy

 

Let B (α, β) be the other end of diameter through A(pq). centers is  and AB = 2r

We know that if a circle touches the axis of x then it is of the form (h,k), k i.e., ordinates of centre = radius 

  

  

or        4qβ = (p – α)2

SIMILAR QUESTIONS

Q1

The length of the longest ray drawn from the point (4, 3) to the circle x2y2 + 16x + 18y + 1 = 0 is equal to

Q2

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  

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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:

Q10

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: