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.

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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 locus 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

               

∴ Centre and radius are (–2, 3) and 2sinα. Respectively.

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.

Testing

SIMILAR QUESTIONS

Q1

For what value of λ will the line = 2x + λ be a tangent to the circle x2 +y2 = 5?

Q2

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

Q3

Find the equation of the tangents to the circle x2 + y2 = 9, which  Are parallel to the line 3x + 4y – 5 = 0

Q4

 

Find the equation of the tangents to the circle x2 + y2 = 9, which

Are perpendicular to the line 2x + 3y + 7 = 0.

Q5

Find the equation of the tangents to the circle x2 + y2 = 9, which make an angle of 60o with the x-axis.

Q6

Show that the line 3x – 4y = 1 touches the circle x2 + y2 – 2x + 4y + 1 = 0. Find the co-ordinates of the point of contact.

Q7

The line (x – 2) cos θ + (y – 2) sin θ = 1 touches a circle for all values of θ. Find the circle.

Q8

 

Find the equation of the normal to the circle

x2 + y2 – 5x + 2y – 48 = 0 at the point (5, 6).

Q9

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

Q10

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