AP EAMCET · Maths · Complex Number
If \(z=x+i y\) and if the point \(P\) in the Argand diagram represents \(z\), then the locus of the point \(P\) satisfying the equation \(2|z-2-3 i|=3|z+i-2|\) is a circle with centre
- A \((10,-21)\)
- B \((-10,21)\)
- C \(\left(2,-\frac{21}{5}\right)\)
- D \(\left(-2, \frac{21}{5}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(2,-\frac{21}{5}\right)\)
Step-by-step Solution
Detailed explanation
\(2| (x-2)+i(y-3) | = 3| (x-2)+i(y+1) |\) \(4((x-2)^2 + (y-3)^2) = 9((x-2)^2 + (y+1)^2)\) \(4(x^2-4x+4+y^2-6y+9) = 9(x^2-4x+4+y^2+2y+1)\) \(4x^2-16x+4y^2-24y+52 = 9x^2-36x+9y^2+18y+45\) \(5x^2 - 20x + 5y^2 + 42y - 7 = 0\) \(x^2 - 4x + y^2 + \frac{42}{5}y - \frac{7}{5} = 0\)…
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