Question

Solution

Correct option is

g2 – f2 = 2c

Equation of common chord is fy – gx = c, equation of the line joining the origin to the points of intersection of the circles is  x2 + y2 + 2g x which are at right angle if

c + c – 2g2 + f2 + g2 = 0 ⇒ g2 – f2 = 2c

SIMILAR QUESTIONS

Q1

If the line 2 (sin a + sin bx – 2 sin (a – by = 3 and 2 (cos a + cos bx + 2 cos (a – by = 5 are perpendicular, then sin 2a+ sin2b is equal to

Q2

If p1p2 denote the lengths of the perpendiculars from the origin on the lines x sec α + y cosec α = 2a and

x cos α + y sin α = a cos 2α respectively, then is equal to

Q3

The locus of the point of intersection of the lines x sin θ + (1 – cos θ) y = a sin θ and x sin θ – (1 + cos θ) y + a sin θ = 0 is

Q4

The straight lines 4x – 3y – 5 = 0, x – 2y – 10 = 0, 7x + 4y – 40 = 0 and x + 3y + 10 = 0 form the sides of a

Q5

If two vertices of a triangle are (5, –1) and (–2, 3), and the orthocenter lies at the origin, the coordinate of the third vertex are

Q6

Equation of a line passing through the intersection of the lines

x + 2y – 10 = 0 and 2x + y + 5 = 0 is

Q7

The lengths of the perpendicular from the points (m2, 2m), (mmm +m) and (m2, 2m) to the line x + y + 1 = 0 form

Q8

The sine of the angle between the pair of lines represented by the equation x2 – 7xy + 12y2 = 0 is

Q9

The square of the differences of the slopes of the lines represented by the equation x2(sec2θ – sin2θ) – (2xy tan θ + y2 sin2θ = 0) is

Q10

Two of the lines represented by x3 – 6x2y + 3xy2 + dy3 = 0 are perpendicular for