GATE XE (Engineering Sciences) 2022 - Question 13

Section: Engineering Mathematics | Marks: 1

If the partial differential equation ሺ𝑥൅2ሻ𝜕ଶ𝑢 𝜕𝑥ଶ൅2ሺ𝑥൅𝑦ሻ𝜕ଶ𝑢 𝜕𝑥 𝜕𝑦൅2ሺ𝑦െ1ሻ𝜕ଶ𝑢 𝜕𝑦ଶെ3𝑦ଶ 𝜕𝑢 𝜕𝑦ൌ0 is parabolic on the circle ሺ𝑥െ𝑎ሻଶ൅ሺ𝑦െ𝑏ሻଶൌ𝑟ଶ, then the values of 𝑎, 𝑏 and 𝑟 are given by

• A. 𝑎ൌ1, 𝑏ൌ2, 𝑟ൌ1
• B. 𝑎ൌെ1, 𝑏ൌ2, 𝑟ൌ1
• C. 𝑎ൌ1, 𝑏ൌെ2, 𝑟ൌ1
• D. 𝑎ൌെ1, 𝑏ൌെ2, 𝑟ൌ1

Answer: B. 𝑎ൌെ1, 𝑏ൌ2, 𝑟ൌ1