First slide

Equation of line in Straight lines

Question

$I f A (\cos α, \sin α), B (\sin α, - \cos α), C (1, 2) a r e t h e v e r t i c e s o f a t r i a n g l e A B C t h e n a s α v a r i e s, t h e l o c u s o f t h e c e n t r o i d o f t h e t r i a n g l e i s k (x^{2} + y^{2}) - 2 x - 4 y + 1 = 0 t h e n k =$

Moderate

A

1
B

2
C

4
D

3

Solution

$E l i m i n a t i n g t h e p a r a m e t e r α, w i l l g e t t h e l o c u s o f t h e c e n t r o i d o f t h e t r i a n g l e$ $\begin{array}{rcl} T h e c e n t r o i d o f t h e t r i a n g l e i s (\frac{\cos α + \sin α + 1}{3}, \frac{\sin α - \cos α + 2}{3}) & = & (x, y) \\ (3 x - 1) & = & \cos α + \sin α \\ (3 y - 2) & = & \sin α - \cos α \\ {(3 x - 1)}^{2} + {(3 y - 2)}^{2} & = & 2 (\cos^{2} α + \sin^{2} α) \end{array}$

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