Question

 

Find the equation of the diameter of the circle

x2 + y2 + 2gx + 2fy + c = 0 which corresponds to the chord ax = by + d= 0.

Solution

Correct option is

bx – ay + bg – af = 0

 

The diameter of circle passes through the centre of the circle and perpendicular to the chord ax + by + d = 0 is  

                           bx – ay + λ = 0                          …(1)

which passes through centre of circle i.e., (–g, –f)

From (1), the equation of the diameter is

            bx – ay + bg – af = 0

SIMILAR QUESTIONS

Q1

 

Find the power of point (2, 4) with respect to the circle 

                x2 + y2 – 6x + 4y – 8 = 0

Q2

Show that the locus of the point, the powers of which with respect to two given circles are equal, is a straight line.

Q3

 

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.

Q4

The chord of contact of tangents drawn from a point on the circle x2 +y2 = a2 to the circle x2 + y2 = b2 touches the circle x2 = y2 = c2. Show that abc are in GP.

Q5

Find the equation of the chord x2 + y2 – 6x + 10y – 9 = 0 which is bisected at (–2, 4).

Q6

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

Q7

Find the locus of middle points of chords of the circle x2 + y2 = a2, which subtend right angle at the point (c, 0).

Q8

Find the equations of the tangents from the point A(3, 2) to the circle x2y2 + 4x + 6y + 8 = 0 .

Q9

If two tangents are drawn from a point on the circle x2 + y2 = 50 to the circle x2 + y2 = 25 then find the angle between the tangents.

Q10

Find the locus of the pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.