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AP EAMCET · Maths · Circle

Let the equation \(\mathrm{ax}^2+2 \mathrm{hxy}+\mathrm{by}^2+2 \mathrm{gx}+2 \mathrm{fy}+\mathrm{c}=0\) represent a point circle other than the origin. Then which one of the following conditions must hold?

  1. A \(b \mathrm{c}>0\)
  2. B \(\mathrm{b}>0\) and \(\mathrm{c} < 0\)
  3. C b \( < 0\) and c \(>0\)
  4. D b \(\leq 0\) and c \( < 0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(b \mathrm{c}>0\)

Step-by-step Solution

Detailed explanation

Given: \(a x^2+2 h x y+b y^2+2 g x+2 f y+c=0 \quad \ldots\) (i) If equation (i) represents a circle, then \(a=b \& h=0\) Then \(\mathrm{eq}^{\mathrm{n}}\) (i) reduces to: \(b x^2+b y^2+2 g x+2 f y+c=0\)…