Question

find length of Latus rectum
4x² +9y2 - 16 x + 54 y + 61 = 0​

Answer 1

Answer:

4x 2 +9y 2+8x+36y+4=0

⇒4(x 2 +2x)+9(y 2 +4y)=−4

⇒4(x 2 +2x+1)+9(y 2 +4y+4)=−4+4+36

⇒4(x+1) 2 +9(y+2) 2 =36

⇒ 9(x+1) 2+ 4(y+2) 2 =1

∴a 2 =9,b 2 =4

Hence length of latus rectum is = a2b 2 = 38

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