Conic Sections Question 1
The centre of the conic represented by the equation $ 2x^{2}-72xy+23y^{2}-4x-28y-48=0 $ is not defined for a general conic section with an xy-term; the centre requires rotation of axes to determine.
Options:
A) $ ( \frac{11}{15},\ \frac{2}{25} ) $
B) $ ( \frac{2}{25},\ \frac{11}{25} ) $
C) $ ( \frac{11}{15},\ -\frac{2}{25} ) $
D) $ ( -\frac{11}{25},\ -\frac{2}{25} ) $
Show Answer
Answer:
Correct Answer: A
Solution:
Centre of conic is $ ( \frac{hf-bg}{ab-h^{2}},\frac{af-gh}{ab-h^{2}} ) $
$ =\frac{(-36)(-14)-(23)(-2)}{(2)(23)-{{(36)}^{2}}},\ \frac{(-2)(-36)-(2)(-14)}{(2)(23)-{{(-36)}^{2}}} $
$ =( -\frac{11}{25},-\frac{2}{25} ) $ .
BETA
