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Circumcentre

If A =6,0, B ...

Question

If $A = (6, 0), B = (0, 8),$ and the circumcenter of the $△ O A B$ where $O$ is the origin, is $(α, β),$ then the value of $α + β$ is

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Solution

Point $A$ lies on $x -$ axis
Point $B$ lies on $y -$ axis
$∴ △ O A B$ is right-angled.
Required point is circumcentre which is the mid-point of $A B$ .
$∴ (α, β) = (3, 4) \Rightarrow α + β = 7$

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A = (6, 0), B = (0, 8),

and the circumcenter of the

△ O A B

O

is the origin, is

(α, β),

then the value of

α + β

O A B C

be a rectangle, where

O

is the origin and

A

C

lie on the parabola

y = x^{2}

B

lies on a parabola whose vertex coordinates is

(α, β)

, then the value of

α + β

α^{2} = 5 α - 3, β^{2} = 5 β - 3

then the value of

\frac{α}{β} + \frac{β}{α}

α \neq β

α

β

γ

are the roots of

x^{3} + a x^{2} + b = 0

, then the value of determinant

Δ

Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} α & β & γ β & γ & α γ & α & β \end{matrix} ∣ ∣ ∣ ∣ ∣

.

α

β

are the zeros of polynomial

x^{2} - a x + b

, then the value of

α^{2} (\frac{α^{2}}{β} - β) + β^{2} (\frac{β^{2}}{α} - α)

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