Question

Find the equation of diameter of the circle x2 + y2 + 2gx + 2fy + c = 0 which corresponds o the chord ax + by + λ = 0. 

Solution

Correct option is

bx – ag + bg – af = 0

 

Any lie parallel to ax + by + λ = 0  

                              bx – ay + λ = 0 

It passes through (–g, –f

So λ = bg – af equation of diameter 

           bx – ag + bg – af = 0

SIMILAR QUESTIONS

Q1

 

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

x2 + y2 – 5x + 2y – 48 = 0   

Q2

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

Q3

 

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.   

Q4

 

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

     2x2 + 2y2 – 7x – 9y – 30 = 0   

Q5

 

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. 

Q6

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.

Q7

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

Q8

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

Q9

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.

Q10

Examine if the two circle x2 + y2 – 2x – 4y = 0 and x2 + y2 – 8y – 4 = 0 touch each other externally or internally. Also the pointed contact.