Question
Download Solution PDFसमीकरण 16(x2 + y2) + 24x + 32y - 9 = 0 द्वारा दर्शाए गए वृत्त की त्रिज्या क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
सामान्य समीकरण 2 + y2 + 2gx + 2fy + c = 0 द्वारा प्रदर्शित वृत्त की त्रिज्या (-g, -f) पर केंद्र के साथ r2 = g2 + f2 - c > 0 द्वारा दी गई है।
गणना:
वृत्त के दिए गए समीकरण को इस प्रकार लिखा जा सकता है:
16(x2 + y2) + 24x + 32y - 9 = 0
⇒ x2 + y2 + \(\frac32\)x + 2y - \(\frac9{16}\) = 0
वृत्त के समीकरण के सामान्य रूप के साथ इसकी तुलना करते हुए, हमारे पास है:
g = \(\frac34\) , f = 1, c = \(-\frac3{16}\)
अब, त्रिज्या = \(\rm\sqrt{g^2+f^2-c}\)
= \(\rm\sqrt{\left(\frac34\right)^2+1^2-\left(-\frac{9}{16}\right)}\)
= \(\rm\sqrt{\frac9{16}+1+\frac{9}{16}}\)
= \(\sqrt{\frac{17}{8}}\)
Last updated on May 31, 2025
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