Find The Middle Point Of The Chord Intercepted On Line lx + my + n = 0 By The Circle x2 + y2 = a2.

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Question

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

Solution

Correct option is

 

Let (x1y1) be the middle point of the chord intercepted by the circle x2y2 = a2 on the line lx + my + n = 0. Then equation of the chord of the circle x2 + y2 = a2, whose middle points is (x1y1), is    

                   

Clearly lx + my + n = 0 and (1) represented the same line,

                    

        

                                    

   

Testing

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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 

Q4

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

Q5

 

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

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

Q6

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

Q7

 

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.

Q8

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.

Q9

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

Q10

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