Question

A diameter of x2 + y2 – 2x – 6y + 6 = 0 is a chord to circle (2, 1), then radius of the circle is 

Solution

Correct option is

3

S1 = x2 + y2 – 2x – 6y + 6 = 0    

or   (1, 3), 2

S2 = (x – 2)2 + (y – 1)2 = r2  

or   x2 + y2 – 4x – 2y + (5 – r2) = 0 

Their common chord is S1 – S2 = 0   

            2x – 4y + (1 + r2) = 0  

This chord being diameter of S1, passes through the centre (1, 3) of S1

∴        r2 = 9                    or        r = 3

SIMILAR QUESTIONS

Q1

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:

Q2

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:

Q3

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

Q4

Let AB be a chord of the circle x2 + y2 = a2 subtending a right angle at the centre. Then the locus of the centroid of the triangle PAB as Pmoves on the circle is

Q5

The lines joining the origin to the points of intersection of the line 4x + 3y = 24 with the circle (x – 3)2 + (y – 4)2 = 25 are

Q6

If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1= 0 intersect in two distinct points P and Q then the line

5x + by – a = 0 passes through P and Q for:  

Q7

The intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of the circle on AB as diameter is:

Q8

A square is formed by following two pairs of straight lines y2 – 14y + 45 = 0 and x2 – 8x + 12 = 0. A circle is inscribed in it. The centre of the circle is 

Q9

Let PQ and RS be tangents at the extremities the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals 

Q10

If α, β, γ, δ be four angles of a cyclic quadrilateral taken in clockwise direction then the value of  will be: