Question

Find the value of k if the lines joining the origin to the points of intersection of the curve 2x²-2xy+3y²+2x-y-1=0 and the line x+2y=k are mutually perpendicular.?​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

Given line 2x²-2xy+3x²+2x-y-1=0

Given curve x+2y=k

X+2y=1

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K

2x²-2xy+3y²+2x(x+2y/k)-y(x+2y/k)-1(x+2y/k)²=0

By solving , We get

x²(2k²+2k-1)+xy(-2k²+3k-4)+(3k²-2k-4)y²=0

:. a+b=0

2k²+2k-1+3k²-2k-4=0

5k²=5

k²=1

k±1

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