Question

 

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. 

Solution

Correct option is

 

Equation of chord of contact of (hk)  

               xh + yk = a2                …(i)

Taking the equation of circle x2 + y2 – a2 = 0 

Homogeneous with the help of xh + yk = a2

            

   

Sub tent 90o at the origin so   

               

∴ Coefficient of x2 + Coefficient of y2 = 0    

  

           

SIMILAR QUESTIONS

Q1

Find the length of intercept on the S.L. 4x – 3y – 10 = 0 by the circle x2y2 – 2x + 4y – 20 = 0.

Q2

Find the coordinates of the middle point of the chord which the circle x2y2 + 4x – 2y – 3 = 0 cut off the line x – y + 2 = 0.   

Q3

For what values of λ will the line y = 2x + λ be a tangent to the circle x2y2 = 5.

Q4

Find the equation of tangent to the circle x2 + y2 – 2ax = 0 at the point  

Q5

Find the equation of normal to the x2 + y2 = 2x which is parallel to x + 2y= 3.  

Q6

 

Find the equation of normal at the point (5, 6) to the circle;

x2 + y2 – 5x + 2y – 48 = 0   

Q7

Find the equation of tangent to the circle x2 + y2 = 16 drawn from the point (1, 4).

Q8

 

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 lows of the point P.   

Q9

 

Find the length of tangents drawn from the point (3, – 4) to the circle

     2x2 + 2y2 – 7x – 9y – 30 = 0   

Q10

The chord of contact of tangents drawn from a point on the circle x2 +y2 = a2 to the circle x2 + y2 = b2 thouchese x2 + y2 = e2 find ab in.