Question

responda

(x+2y)²=
(4w+35)²=
(5x-y)²=
(p-q)²=
(m+n)(m-n)=

Answer 1

tan(theta) = -1
definition of tangent is opposite/adjacent, or you can say change in y divided by change in x
so tan(theta) = dy/dx

x²y² + xy = 2
x²(2y)(dy/dx) + y²(2x) + x(dy/dx) + y(1) = 0
2x²y(dy/dx) + 2xy² + x(dy/dx) + y = 0
(dy/dx)(2x²y + x) = -2xy² - y
-(2x²y + x) = -2xy² - y
2x²y + x = 2xy² + y
2x²y - 2xy² = -x + y
2xy(x - y) = -(x - y)
2xy(x - y) + (x - y) = 0
(x - y)(2xy + 1) = 0
x = y or xy = -1/2

substitute x = y into general equation
x⁴ + x² = 2
x⁴ + x² - 2 = 0
(x² - 2)(x² + 1) = 0
x ∈ ℝ
x = √2, -√2
y = √2, -√2

substitute xy = -1/2 into general equation
(-1/2)² + (-1/2) = -1/4 ≠ 2
so xy = -1/2 is not a solution

hence the points are (√2, √2) and (-√2, -√2)



note that Ed I have different answer with mine because he (or she) saw x^2 y^2 as x^2 + y^2