Find The Area Of An Equilateral Triangle Inscribed In The Circle                        x2 + y2 + 2gx + 2fy + c = 0     

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Question

 

Find the area of an equilateral triangle inscribed in the circle

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

Solution

Correct option is

None of these

 

Given circle is

              x2 + y2 + 2gx + 2fy + c = 0                    …(1)

Let O be the centre and ABC be an equilateral triangle inscribed in the circle (1).

                        O ≡ (–g, –f)

 

                                         

                                         

Testing

SIMILAR QUESTIONS

Q1

If P is taken to be at (h, 0) such that P’ lies on the circle, the area of the rhombus is

Q2

Locus of mid-point of the chords of contact of x2 + y2 = 2 from the points on the line 3x + 4y = 10 is a circle with centre P. If O be the origin then OP is equal to

Q3

Suppose ax + bx + c = 0, where abc are in A.P. be normal to a family or circles. The equation of the circle of the family which intersects the circle x2 + y2 – 4x – 4y – 1 = 0 orthogonally is

Q4

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

Q5

Find the equation of that chord of the x2 + y2 = 15 which is bisected at (3, 2).

Q6

 

Find the centre and radius of the circle 

             2x2 + 2y2 = 3x – 5y + 7

Q7

Find the equation of the circle whose centre is the point of intersection of the lines 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 and passes through the origin.

Q8

Find the equation of the circle concentric with the circle x2 + y2 – 8x + 6y– 5 = 0 and passing through the point (–2, –7).

Q9

A circle has radius 3 units and its centre lies on the line y = x – 1. Find the equation of the circle if it passes through (7, 3).

Q10

 

Find the parametric form of the equation of the circle

                               x2 + y2 + px + py = 0