Question

if the equation ax^2+3xy-2y^2-5x+5y+c=0 represents a pair of perpendicular straight line. find a and c

Answer 1

Step-by-step explanation:

Given if the equation ax^2+3xy-2y^2-5x+5y+c=0 represents a pair of perpendicular straight line. find a and c

• So given equation is ax^2 + 3xy – 2y^2 – 5x + 5y + c = 0
• Comparing with ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 we get
•   a = 2, 2h = 3, h = 3/2, b = -2, 2g = - 5 g = - 5/2, 2f = 5, f = 5/2, c = c
• So the given equation represents a pair of lines  perpendicular to each other we get
•        So coefficient of x^2 + coefficient of y^2 = 0
•        So  a + (- 2) = 0
•         So a = 2
• Also equation represents a pair of lines.
•       So      a     h      g
•                 h      b      f  = 0
•                g       f       c
•  
•                 2      3/2    - 5/2
•                3/2     - 2      5/2  = 0
•                -5/2     5/2     c
• 2(- 2c – 25/4) – 3/2 (3c / 2 + 25/4) – 5/2(15/4 – 10/2)
• -8c – 25/2 – 18c – 75 / 8 + 25 / 8
•        -50 c – 150 = 0
•         -50 c = 150
•         Or c = - 150 / 50
•              c = - 3
• Therefore a = 2 and c = - 3

Reference link will be

https://brainly.in/question/17339055