Question

If a line segment AM = a moves in the plane XOY remaining parallel toOX so that the left end point A slides along the circle x2 + y2 = a2, the locus of M is

Solution

Correct option is

x2 + y2 = 2ax

Let the coordinates of A be (xy) and M be (α, β) (Fig.).

Since AM is parallel to OX,  

α = x + a and β = y      ⇒     x = α – a and y = β

As A(xy) lies on the circle x2 + y2 = a2 we have 

                                       

 
                                                    

 

 

SIMILAR QUESTIONS

Q1

Three circles with radii 3 cm, 4 cm and 5 cm touch each other externally. If A is the point of intersection of tangents to these circles at their points of contact, then the distance of A from the points of contact is

Q2

A line meets the coordinate axes in A and B. A circle is circumscribed about the triangle OAB. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively, the diameter of the circle is

Q3

 

If a circle passes through the point (ab) and cuts the circle x2 + y2 = k2 orthogonally, equation of the locus of its centre is

Q4

Equation of the circle which passes through the origin, has its centre on the line x + y = 4 and cuts the circle

x2 + y2 – 4x + 2y + 4 = 0 orthogonally, is

Q5

If O is the origin and OPOQ are distinct tangents to the circle x2 + y2 + 2gx + 2fy + c = 0, the circumcentre of the triangle OPQ is

Q6

The circle passing through the distinct points (1, t), (t, 1) and (tt) for all values of t, passes through the point

Q7

If OA and OB are the tangents from the origin to the circle x2 + y2 + 2gx + 2fy + c = 0, and C is the centre of the circle, the area of the quadrilateral OACB is 

Q8

The angle between a pair of tangents drawn from a point P to the circle x2 + y2 + 4x – 6y + 9 sin2α + 13 cos2α = 0 is 2α. The equation of the locus of the point P is

Q9

Equation of a circle through the origin and belonging to the co-axial system, of which the limiting points are (1, 2), (4, 3) is

Q10

If common chord of the circle C with centre at (2, 1) and radius r and the circle x2 + y2 – 2x – 6y + 6 = 0 is a diameter of the second circle, then the value of r is