Question

The circle x2 + y2 + x + y = 0 and x2 + y2 + x – y = 0 intersect at the angle of:

Solution

Correct option is

π/2

Equation of the given circles are  

                   x2 + y2 + x + y = 0                  …(1)  

                   x2 + y2 + x – y = 0                  …(2)  

Comparing (1) & (2) with  

                   x2 + y2 + 2gx + 2fy + c = 0  

                

            

  

  

Radius of the circle (1) is 

                                              

                                              

Radius of the circle (2) is   

            

                             

   

                          = 0   

                 

                         

SIMILAR QUESTIONS

Q1

If α, β, γ, δ be four angles of a cyclic quadrilateral taken in clockwise direction then the value of  will be:

Q2

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

Q3

A circle passes through the point (–1, 7) and touches the line y = x at (1, 1). Its diameter is

Q4

Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is

Q5

Let a circle be given by 2x(x – a) + y(2y – b) = 0, (a  0, b ≠ 0). Find the condition on a and b, if two chords each bisected by the x – axis can be drawn to the circle from 

Q6

The equation of the locus of the mid points of the chords of the circle 4x2 + 4y2 – 12x + 4y + 1 = 0 that subtend an angle of  at its centre is:

Q7

Find the radius of the smallest circle which touches the straight line 3x– y = 6 at (1, –3) and also touches the line y = x. complete up to one place of decimal.

Q8

Let S  x2 + y2 + 2gx + 2fy + c = 0 be a given circle. find the locus of the foot of the perpendicular drawn from the origin upon any chord of S which subtends a right angle at the origin.

Q9

The normal 3x – 4y = 4 and 6x – 8y – 7 = 0 are tangents to the circle. Then its radius is:

Q10

Find the radical centre of the circles, x2 + y2 + 3x + 2y + 1 = 0,  x2 + y2 – x + 6y + 5 = 0, x2 + y2 + 5x – 8y + 15 = 0