TS EAMCET · Maths · Circle
For the circles \((x-a)^2+y^2=a^2\) and \(x^2+(y-a)^2=a^2\), where \(a>0\), which one of the following is not true?
- A mid-point of the common chord is \(\left(\frac{a}{2}, \frac{a}{2}\right)\)
- B length of the common chord is \((\sqrt{2} a)\)
- C the circles intersect at \((0,0)\) and \((a, a)\)
- D common chord is at a distance of \((\sqrt{2 } a)\) units from the centres of given circles
Answer & Solution
Correct Answer
(D) common chord is at a distance of \((\sqrt{2 } a)\) units from the centres of given circles
Step-by-step Solution
Detailed explanation
Given, circle \((x-a)^2+y^2=a^2 \text { and } x^2+(y-a)^2=a^2\) Common chord of circle is \((x-a)^2-x^2+y^2-(y-a)^2=0\) \(\begin{aligned} & \Rightarrow(x-a-x)(x-a+x)+(y+y-a)(y-y+a)=0 \\ & \Rightarrow(2 x-a)-(2 y-a)=0 \Rightarrow x-y=0 \end{aligned}\) \(\therefore\) End point of…
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