Question

A point moves such that the sum of the squares of its distances from the sides of a square of side unity is equal to 9. The locus of such a point is a circle

Solution

Correct option is

Containing the square

The sides of the square be x = 0, x = 1, y = 0, y = 1(hk) be any point on the locus, then 

   

   

Locus x2 + y2 – x – y – 7/2 = 0 is a circle with centre (1/2, 1/2), the centre of the square and radius equal to 4, greater than the diagonal of the square and hence contains the square.

SIMILAR QUESTIONS

Q1

The locus of the point which moves in a plane so that the sum of the squares of its distances from the lines ax + by + c = 0 and

bx – ay + d = 0 is r2, is a circle of radius.  

 

Q2

The locus of the centre of the circle passing through the origin O and the points of intersection of any line through (ab) and the coordinates axis is a

Q3

Four distinct point (1, 0), (0, 1), (0, 0) and (tt) are concyclic for

Q4

If two circles which pass through the points (0, a) and (0, –a) cut each other orthogonally and touch the straight line 

y = mx + c, then

Q5

The coordinates of two point P and Q are (2, 3) and (3, 2) respectively. Circles are described on OP and OQ as diameters; O being the origin, then length of the common chord is

Q6

The circle x2 + y2 – 6x – 4y + 9 = 0 bisects the circumference of the circle x2 + y2 – (λ + 4)x – (λ + 2)y + (5λ + 3) = 0 if λ is equal to

Q7

The locus of the middle points of the chords of the circle of radius which subtend an angle π/4 at any point on the circumference of the circle is a concentric circle with radius equal to

Q8

The lengths of the tangents from two points A and B to a circle are l and l’ respectively. If the points are conjugate with respect to the circle, then (AB)2 is equal to

Q9

If two circles, each of radius 5 units, touch each other at (1, 2) and the equation of their common tangent is 4x + 3y = 10, then equation of the circle, a portion of which lies in all the quadrants is

Q10

Radical centre of the three circles x2 + y2 = 9, x2 + y2 – 2x – 2y = 5, x2 + y2 + 4x + 6y = 19 lies on the line y = mx if m is equal to