AP EAMCET · Maths · Circle
Choose the correct option regarding the following statements :
Statement I The length of common chord of the circles \(x^2+y^2+a x+b y+c=0\) and
\(x^2+y^2+b x+a y+c=0\) equals \(\frac{\sqrt{(a+b)^2-8 c}}{2}\)
Statement II If two circles intersect at two distinct points, then their radical axis is their common chord.
- A Both statements are true and statement-II is a correct explanation for statement-I.
- B Both statements are true but statement-II is not a correct explanation for statement-I.
- C Statement-I is true, Statement-II is false.
- D Statement-I is false, Statement-II is true.
Answer & Solution
Correct Answer
(D) Statement-I is false, Statement-II is true.
Step-by-step Solution
Detailed explanation
Statement I The length of common chord of the circles \(x^2+y^2+a x+b y+c=0\) and \(x^2+y^2+b x+a y+c=0\) equals \(\frac{\sqrt{(a+b)^2-8 c}}{2}\) Let the circles \(\mathcal{c}_1\) be the center of \(x^2+y^2+a x+b y+c=0\) ...(i) and \(c_2\) be the center of…
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