Question

Coordinates of the foci of the ellipse
5x2 +9y2 +10x - 36y -4 = 0 are
A) (1, 2) and (-3,2)
B) (2, 1) and (-3,2)
C) (1, 2) and (3, 2)
D) none of these​

Answer 1

the coordinates of the foci are  (1  , 2)  & (- 3 , 2)  for 5x²  + 9y² + 10x  - 36y  - 4  =0

Step-by-step explanation:

5x²  + 9y² + 10x  - 36y  - 4  =0

=> (√5x  + √5)² - 5  + (3y  - 6)² - 36 - 4 =0

=> (√5x  + √5)²  +  (3y  - 6)² = 45

=>   (√5x  + √5)² /45  +  (3y  - 6)²/45 = 1

=> (x + 1)²/9  +  (y - 2)²/5  = 1

=> (x + 1)²/3²   +  (y - 2)²/(√5)² = 1

Comparing with

(x - h)²/a²  + (y - k)²/b² = 1

h = - 1   ,  k =  2     a² = 9  b² = 5

c² = a² - b² = 9 - 5   => c = ±2

the coordinates of the foci are  ( h ± c , k)

(1  , 2)  & (- 3 , 2)

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