Question

3. Find the angle between the lines joining the origin to the points of intersection of the curve x²+2xy+y²+2x+2y-5=0
and the line 3x - y + 1 = 0.​

Answer 1

Step-by-step explanation:

Given equations of curve and the line are 2x

2

+3xy−4x+1=0 and 3x+y=1.

Homogenising the curve with the line gives

2x

2

+3xy−4x(3x+y)+(3x+y)

2

=0

⇒2x

2

+3xy−12x

2

−4xy+9x

2

+y

2

+6xy=0

⇒y

2

−x

2

+5xy=0