Question

Find the equation of the tangents from the point A(3, 2) to the circle x2 +y2 + 4x + 6y + 8 = 0.

Solution

Correct option is

2x – y – 4 = 0 and x – 2y + 1 = 0

 

 2x2 + 2y2 – 5xy – 2x + 7y – 4 = 0   

or      (2x – y – 4) (x – 2y + 1) = 0

here  2x – y – 4 = 0 and x – 2y + 1 = 0  

Alternative:-

Let the equation be

                   y – 2 = m(x – 2) 

                  mx – y + 2 – 3m = 0                  …(i)

Length of perpendicular from c(–2, –3) on equation (1) = radius of circle.

                      

Put in equation (1) to get 2x – y – 4 = 0 and x – 2y + 1 = 0   

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

 

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

x2 + y2 – 5x + 2y – 48 = 0   

Q4

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

Q5

 

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.   

Q6

 

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

     2x2 + 2y2 – 7x – 9y – 30 = 0   

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 thouchese x2 + y2 = e2 find ab in.

Q9

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

Q10

If two tangents are drawn from a point on the circle x2 + y2 = 25 to the circle x2 + y2 = 25. Then find the angle between the tangents.