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AP EAMCET · Maths · Circle

Suppose that the \(x\)-coordinates of the points \(A\) and \(B\) satisfy \(x^2+2 x-a^2=0\) and their \(y\)-coordinates satisfy \(y^2+4 y-b^2=0\). Then, the equation of the circle with \(A B\) as its diameter is

  1. A \(x^2+y^2+2 x+4 y-a^2-b^2=0\)
  2. B \(x^2+y^2+2 x+4 y+a^2+b^2=0\)
  3. C \(x^2+y^2-2 x-4 y-a^2-b^2=0\)
  4. D \(x^2+y^2-2 x-4 y+a^2+b^2=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(x^2+y^2+2 x+4 y-a^2-b^2=0\)

Step-by-step Solution

Detailed explanation

Let \(x_1\) and \(x_2\) are roots of equation \(x^2+2 x-a^2=0\) and \(y_1\) and \(y_2\) are roots of equation \(y^2+4 b-b^2=\left(x-x_1\right)\left(x-x_2\right)=0\) and \(y^2+4 b-b^2 \rightarrow y_1, y_2\) \(=\left(y-y_1\right)\left(y-y_2\right)\) (roots of equation) Let…