Question

the three roots of a equivalent triangle 3x ^3+px^2+qx-4 are the side length in radius and the circum radius of an equilateral triangle then the value of /2p+q/​

Answer 1

Answer:

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>>If the equation of the incircle of an eq

Question

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If the equation of the incircle of an equilateral triangle is x

2

+y

2

+4x−6y+4=0, then the equation of the circumcircle of the triangle is

Medium

Solution

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Correct option is B)

Given equation of the incirle is x

2

+y

2

+4x−6y+4=0

Its incenter is (−2,3) and inradius =

4+9−4

=3

Since in an equilateral triangle, the incenter and the circumcenter coincide,

∴ Circumcenter =(−2,3)

Also, in an equilateral triangle, circumradius =2( inradius)

∴ Circumradius =2.3=6

∴ The equation of the circumcircle is

(x+2)

2

+(y−3)

2

=(6)

2

⇒x

2

+y

2

+