Question

If the lines 3x – 4y – 7 = 0 and 2x – 3y – 5 = 0 are two diameters of a circle of area 49π square units, then the equation of the circle is:

Solution

Correct option is

x2 + y2 – 2x + 2y – 47 = 0

Centre is (1, –1) the point of intersection of diameters. Area ⇒

r = 7. Hence its equation is (x – 1)2 + (y + 1)2 = 49.

SIMILAR QUESTIONS

Q1

A circle passes through the origin O and cuts the axis at A(a, 0) and B(0,b). The reflection of O in the line AB is the point

Q2

The length of the longest ray drawn from the point (4, 3) to the circle x2y2 + 16x + 18y + 1 = 0 is equal to

Q3

1:- The chords in which the circle C cuts the members of the family S of circles through A and B are con-current at  

Q4

2:- Equations of the member of the family S which bisects the circumference of C is

Q5

3:- If O is the origin and P is the centre of C, then the difference of the squares of the lengths of the tangents from A and B to the circle is equal to

Q6

If the two (x – 1)2 + (y – 3)2 = r2 and x2 + y2 – 8x + 2y + 8 = 0 intersect in two distinct points, then

Q7

The distance between the chords of contact of the tangent to the circle x2 + y2 + 2gx + 2fy + c = 0 from the origin and the point (gf) is

Q8

The angle between the tangents drawn from the origin to the circle (x – 7)2 + (y + 1)2 = 25 is

Q9

A square is inscribed in the circle x2 + y2 – 2x + 4y + 3 = 0. Its sides are parallel to the co-ordinates axes. Then one vertex of the square is

Q10

A variable circle passes through a fixed point A(pq) and touches the x-axis. The locus of the other end of the diameter through A is: