Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

show that the lines x2-4xy+y2=0 and x+y=3 form an equilateral triangle also find area of the triangle

Sagot :

Given pair of lines are x² + 4xy + y² = 0

⇒ (y/x) ² + 4 y/x + 1 = 0

⇒ y/x = -4±2√3/2 = -2±√3,

∴  The lines y = (-2 + √3) x and y = (-2 - √3) x and x - y = 4 forms an equilateral triangle

Clearly the pair of lines x² + 4xy +y²  = 0  intersect at origin,

The perpendicular distance form origin to x - y = 4 is the height of the

h = 2 √ 2

∵ Area of triangle = h²/√3 = 8/√3

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.