Question
Download Solution PDFलैटस रेक्टम के छोर से परवलय x2 = 20y के शीर्ष को जोड़ने वाली रेखाओं द्वारा निर्मित त्रिभुज का क्षेत्रफल क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
Y - अक्ष के साथ परवलय का समीकरण: (x – h)2 = ±4a (y - k),
यहाँ, बिंदु (h, k) परवलय का शीर्ष है, 4a = लैटस रेक्टम की लम्बाई और केंद्र बिंदु (0, ±a)
गणना:
दिया गया परवलय: x2 = 20y
x2 = 4ay ⇒ a = 5 और शीर्ष = (0, 0)
∴ केंद्र बिंदु = (0, 5)
x2 = 20(5) = 100
⇒ x = ± 10
AB = 10 + 10 = 20
OM = 5
∴ त्रिभुज का क्षेत्रफल OAB = ½ × आधार × ऊंचाई
= 1/2 × (20) × (5)
= 50 वर्ग इकाई
अतः विकल्प (4) सही है।
Last updated on May 30, 2025
->UPSC has released UPSC NDA 2 Notification on 28th May 2025 announcing the NDA 2 vacancies.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced for cycle 2. The written examination will be held on 14th September 2025.
-> Earlier, the UPSC NDA 1 Exam Result has been released on the official website.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.