AP EAMCET · Maths · Straight Lines
The locus of the third vertex of a right-angled triangle, the ends of whose hypotenuse are \((1,2)\) and \((4,5)\), is
- A \(x^2+y^2+5 x+7 y+14=0\)
- B \(3 x+3 y-1=0\)
- C \(3 x+3 y+1=0\)
- D \(x^2+y^2-5 x-7 y+14=0\)
Answer & Solution
Correct Answer
(D) \(x^2+y^2-5 x-7 y+14=0\)
Step-by-step Solution
Detailed explanation
Let the third vertex be \( (x,y) \). The slopes of the legs are \( m_1 = \frac{y-2}{x-1} \) and \( m_2 = \frac{y-5}{x-4} \). \( m_1 m_2 = -1 \) \( \left(\frac{y-2}{x-1}\right) \left(\frac{y-5}{x-4}\right) = -1 \) \( (y-2)(y-5) = -(x-1)(x-4) \) \( y^2-7y+10 = -(x^2-5x+4) \)…
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