QJEEAdv21Ma0a6e: JEE Advanced 2021 Mathematics - Class 11 JEEAdv21Ma0a6e Solution: Consider a triangle Δ whose two sides lie on the x-axis and the …

Question

Verified Solution • 2025–26 Session moderate

Consider a triangle

Δ

whose two sides lie on the x-axis and the line x + y + 1 = 0. If the orthocenter of

Δ

is (1, 1), then the equation of the circle passing through the vertices of the triangle

Δ

is

Accepted Answer

Equation of circle passing through C(0, 0) is

x² + y² + 2gx + 2fy = 0 ..... (i)

Since Eq. (i), also passes through (

-

1, 0) and (1,

-

2).

Then, 1

-

2g = 0

\Rightarrow

g = 1 / 2

and 5 + 1

-

4f = 0

\Rightarrow

f = 3 / 2

∴

Equation of circumcircle is x² + y² + 2

\times

\frac{1}{2}

x + 2

\times

\frac{3}{2}

y = 0

i.e. x² + y² + x + 3y = 0

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