AP EAMCET · Maths · Pair of Lines
Suppose that the sides passing through the vertex \((\alpha, \beta)\) of a triangle are bisected at right angles by the lines \(y^2-8 x y-9 x^2=0\). Then, the centoid of the triangle is
- A \(\frac{1}{123}(\alpha, \beta)\)
- B \(\frac{1}{123}(\alpha+32 \beta, \beta+32 \alpha)\)
- C \(\frac{1}{123}(\alpha-32 \beta, \beta+32 \alpha)\)
- D \(\frac{1}{123}(\alpha-32 \beta, \beta-32 \alpha)\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{123}(\alpha-32 \beta, \beta-32 \alpha)\)
Step-by-step Solution
Detailed explanation
\(y^2-8 x y-9 x^2=0\) \(y^2-9 x y+x y-9 x^2=0\) \((y-9 x)(y+x)=0\) The two given lines are \(y=9 x\) and \(y=-x\) Slope of line \(y=9 x\) is 9 and slope of line \(y=-x\) is -1 . Let \(A B\) and \(B C\) be the line perpendicular to \(y=9 x\) and \(y=-x\) respectively. Slope of…
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