Question

Find the locus of middle points of chords of the circle x2 + y2 = a2, which subtend right angle at the point (c, 0).

Solution

Correct option is

2(x2 + y2) – 2cx + c2 – a2 = 0

 

Let N (hk) be the middle point of any chord AB, which subtend a right angle at P(c, 0).

    

(since distance of the vertices from middle point of the hypotenuse are equal)

  

or                                            

∴ Locus of N(hk) is  

             2(x2 + y2) – 2cx + c2 – a2 = 0

 

 

SIMILAR QUESTIONS

Q1

Find the length of the tangents drawn from the point (3, – 4) to the circle 2x2 + 2y2 – 7x – 9y – 13 = 0.

Q2

Find the area of the triangle formed by tangents from the point (4, 3) to the circle x2 + y2 = 9 and the line segment joining their points of contact is 

Q3

Find the length of the tangent from any point on the circle x2 + y2 + 2gx+ 2fy + c = 0 to the circle x2 + y2 + 2gx + 2fy + c1 = 0 is

Q4

 

Find the power of point (2, 4) with respect to the circle 

                x2 + y2 – 6x + 4y – 8 = 0

Q5

Show that the locus of the point, the powers of which with respect to two given circles are equal, is a straight line.

Q6

 

Find the condition that chord of contact of any external point

(hk) to the circle x2 + y2 = a2 should subtend right angle at the centre of the circle.

Q7

The chord of contact of tangents drawn from a point on the circle x2 +y2 = a2 to the circle x2 + y2 = b2 touches the circle x2 = y2 = c2. Show that abc are in GP.

Q8

Find the equation of the chord x2 + y2 – 6x + 10y – 9 = 0 which is bisected at (–2, 4).

Q9

Find the middle point of the chord intercepted on line lx + my + n = 0 by the circle x2 + y2 = a2.

Q10

Find the equations of the tangents from the point A(3, 2) to the circle x2y2 + 4x + 6y + 8 = 0 .