Question

find the asymptot of the curve (2x-3y+1)²(x+y)-8x+2y-9=0​

Answer 1

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Answer 2

Given: (2x-3y+1)²(x+y)-8x+2y-9=0​

To Find: value of asymptote

Solution:

The equation of asymptotes and the curve only differ by constant. So the combined equation of asymptotes is

(2x-3y+1)²(x+y)-8x+2y-9=0

It represents a pair of straight lines

∴abc+2fgh−af ^2−bg^2 −ch^2 =0

4c+25−25/2 −8− 25C/4 =0

16c+100−50−32−25c=0

c=2

So, the equation of asymptotes is

2x ^2 +5xy+2y ^2 +4x+5y+2=0

2y ^2+(5x+5)y+2x ^2 +4x+2=0

Y= −(5x+5)± $\sqrt{x} (5x+5) 2 −4(2)(2x 2 +4x+2)$/ 4

4y+5x+5=±$\sqrt{x} 9x 2 +9−18x​$

4y+5x+5=±(3x−3)

⇒4y+5x+5=3x−3

⇒2x+4y+8=0

⇒4y+5x+5=−(3x−3)

⇒8x+4y+2=0

(2x+4y+8)(8x+4y+2)=0

The value of asymptote is c=2

The eqauation of asymptote is (2x+4y+8)(8x+4y+2)=0

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