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<div><span style="font-family: Times New Roman; font-size: 13px;"> </span> <p style="margin: 0in 0in 0pt; line-height: normal;"><span style="color: black; mso-fareast-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;;"><span style="font-family: Calibri; font-size: 13px;">The centers of the circles touching both the coordinate axes lies on the line </span></span></p> <p style="margin: 0in 0in 0pt; line-height: normal;"><span style="color: black; mso-fareast-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;;"><span style="font-family: Calibri; font-size: 13px;">x &ndash; y = 0 or x + y = 0 according to the quadrant in which the circle lies. </span></span></p> <p style="margin: 0in 0in 0pt; line-height: normal;"><span style="color: black; mso-fareast-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;;"><span style="font-family: Calibri; font-size: 13px;">Based on this data answer the following 2 questions.</span></span></p> <span style="font-family: Times New Roman; font-size: 13px;"> </span> <p style="margin: 0in 0in 0pt; line-height: normal;"><span style="color: black; mso-fareast-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;;"><span style="font-family: Calibri; font-size: 13px;">&nbsp;</span></span></p> <span style="font-family: Times New Roman; font-size: 13px;"> </span> <p style="margin: 0in 0in 0pt; line-height: normal;"><span style="color: black; mso-fareast-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;;"><span style="font-family: Calibri; font-size: 13px;">A) If the difference between the radii of the circles passing through (a, b) and touching the axes is </span></span><span style="color: black; mso-fareast-font-family: &quot;Times New Roman&quot;; mso-bidi-font-family: &quot;Times New Roman&quot;;"><span style="font-family: Calibri; font-size: 13px;">C &gt; 0 and a, b &gt;&nbsp;0 then the least value of a + b is</span></span><span style="font-family: Times New Roman; font-size: 13px;"> </span></p> <p style="margin: 0in 0in 0pt; line-height: normal;"><img class="Wirisformula" alt="1 right parenthesis thin space space c space space space space space space space space space space space space space space space space 2 right parenthesis space square root of 2 c space space space space space space space space space space space 3 right parenthesis thin space fraction numerator c over denominator square root of 2 end fraction space space space space space space space space space 4 right parenthesis space 2 c" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=e85b9bd04a29c16e0c8da4ef8094b353.png" align="middle" /></p> <p style="margin: 0in 0in 0pt; line-height: normal;"></p> <p style="margin: 0in 0in 0pt; line-height: normal;"><span style="font-family: Times New Roman; font-size: 13px;"><span style="line-height: 107%; font-family: &quot;Calibri&quot;,sans-serif; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;">B) If one of the points of intersection of the two circles touching the axes is (p,q) then the length of the common chord is </span></span></p> <p style="margin: 0in 0in 0pt; line-height: normal;"></p> <p style="margin: 0in 0in 0pt; line-height: normal;"><span style="font-family: Times New Roman; font-size: 13px;"><span style="line-height: 107%; font-family: &quot;Calibri&quot;,sans-serif; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;"><img class="Wirisformula" alt="1 right parenthesis thin space vertical line p plus-or-minus q vertical line space space space space space space space space space 2 right parenthesis space square root of 2 vertical line p plus-or-minus q vertical line space space space space space space space space space space space 3 right parenthesis space 2 vertical line p plus-or-minus q vertical line space space space space space space space space space space 4 right parenthesis space square root of 2 space vertical line p q vertical line" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=3366b10c5b5e0bd9bbf89021fa32cbeb.png" align="middle" /><br /></span></span></p> </div>
Asked by Sunil Soni | 10 Aug, 2016, 07:24: PM

Answered by Vijaykumar Wani | 12 Aug, 2016, 04:52: PM

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