TS EAMCET · Maths · Straight Lines
If the points \(\mathrm{A}(2,3), \mathrm{B}(3,2)\) form a triangle with a variable point \(\mathrm{p}\left(\mathrm{t}, \mathrm{t}^2\right)\), where t is a parameter, then the equation of the locus of the centroid of triangle ABC is
- A \(9 x^2-30 x-3 y+20=0\)
- B \(3 x^2-10 x-y+10=0\)
- C \(9 y^2-30 y-3 x+20=0\)
- D \(3 y^2-10 y-x+10=0\)
Answer & Solution
Correct Answer
(B) \(3 x^2-10 x-y+10=0\)
Step-by-step Solution
Detailed explanation
Let the centroid be \( (x, y) \). \( x = \frac{2+3+t}{3} = \frac{5+t}{3} \) \( y = \frac{3+2+t^2}{3} = \frac{5+t^2}{3} \) From the first equation: \( t = 3x - 5 \) Substitute t into the second equation: \( 3y = 5 + (3x-5)^2 \) \( 3y = 5 + 9x^2 - 30x + 25 \)…
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