Question
If x ma + y nb =1 touches the ellipse x^ 2 a^ 2 + y^ 2 b^ 2 =1, then
BITSAT
Mathematics
Ellipse
2020
BITSAT 2020
BITSAT Mathematics Question (2020) — Solution
Options
- A. m ^ 2 = n ^ 2 n ^ 2 -1 or n ^ 2 = m ^ 2 ~m ^ 2 -1
- B. m ^ 2 = n ^ 2 n ^ 2 +1 or n ^ 2 = m ^ 2 ~m ^ 2 +1
- C. m ^ 2 = n ^ 2 +1 n ^ 2 or n ^ 2 = m ^ 2 +1 ~m ^ 2
- D. m ^ 2 = n ^ 2 -1 n ^ 2 or n ^ 2 = m ^ 2 -1 ~m ^ 2
Answer
A. m ^ 2 = n ^ 2 n ^ 2 -1 or n ^ 2 = m ^ 2 ~m ^ 2 -1
Step-by-step solution
The line is y=- nb ma x-n b. It will touch the ellipse if (-n b)^ 2 =a^ 2 (- n b m a )^ 2 +b^ 2 [ c ^ 2 = a ^ 2 ~m ^ 2 + b ^ 2 ] n^ 2 = n^ 2 m^ 2 +1 m ^ 2 = n ^ 2 n ^ 2 -1 or n ^ 2 = m ^ 2 ~m ^ 2 -1
Related: Mathematics — Ellipse · All PYQ Banks