Straight Line Question 147
Question: The line $ \frac{x}{a}+\frac{y}{b}=1 $ meets the x-axis at A, the y-axis at B, and the line y=x at C such that the area of $ \Delta AOC $ is twice the area of $ \Delta BOC $ . Then the coordinates of C are
Options:
A) $ ( \frac{b}{3},\frac{b}{3} ) $
B) $ ( \frac{2a}{3},\frac{2a}{3} ) $
C) $ ( \frac{2b}{3},\frac{2b}{3} ) $
D) none of these
Correct Answer: C [c] Given $ ar\Delta AOC=2(ar\Delta BOC) $ Or $ \frac{1}{2}(OA)(x_1)=\frac{2\times 1}{2}(OB)(x_1) $ Or $ a=2b $ The equation of AB is $ \frac{x}{a}+\frac{y}{b}=1 $ …(i) Or $ \frac{x}{2b}+\frac{y}{b}=1 $ …(ii) Since point C lies on line (ii), we have $ \frac{x_1}{2b}+\frac{y_1}{b}=1 $ Or $ x_1=\frac{2b}{3}=\frac{a}{3} $ Or $ C\equiv ( \frac{2b}{3},\frac{2b}{3} ) $
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Answer:
Solution:
BETA
