Question

 

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.   

Solution

Correct option is

(x + 2)2 + (y – 3)2 = 4

 

Let co-ordinates of P be (x1y1) and given circle is

        x2 + y2 + 4x – 6y + 9 sin3α + 13 cos2α = 0    

  

  

  

Distance between P(x1y1) and centre of circle C (–2, 3) is   

      

  

The required locus of P(x1y1) is  

        (x + 2)2 + (y – 3)2 = 4

SIMILAR QUESTIONS

Q1

 

Discus the position of the points (1, 2) and (6, 0) with respect to the circle.

                 x2 + y2 – 4x + 2y – 11 = 0   

Q2

 

Find the shortest and largest distance from the point (2, –7) to the circle 

                 x2 + y2 – 14x – 10y – 151 = 0   

Q3

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

Q4

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.   

Q5

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

Q6

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

Q7

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

Q8

 

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

x2 + y2 – 5x + 2y – 48 = 0   

Q9

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

Q10

 

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

     2x2 + 2y2 – 7x – 9y – 30 = 0