Question
Download Solution PDFयदि z = x + iy है, जहाँ i = √-1 है, तो समीकरण zz̅ + ∣z∣2 + 4(z + z̅) - 48 = 0 क्या निरूपित करता है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFप्रयुक्त सूत्र:
z = a + ib
वृत्त का समीकरण: (x - h)2 + (y - k)2 = r2
जहाँ (h,k) वृत्त के केंद्र के निर्देशांक हैं और r त्रिज्या है।
गणना:
(x + iy)(x - iy) + x2 + y2 + 4(x + iy + x - iy) - 48 = 0
⇒ x2 + y2 + x2 + y2 + 4 × 2x - 48 = 0
⇒ 2(x2 + y2) + 8x - 48 = 0
⇒ x2 + y2 + 4x - 24 = 0
⇒ (x + 2)2 + (y - 0)2 =
चूंकि, उपरोक्त समीकरण (x - h)2 + (y - k)2 = r2 के समान है
∴ दिया गया समीकरण एक वृत्त का प्रतिनिधित्व करता है।
Last updated on May 30, 2025
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