The line  intersects the curve xy = c2, z = 0 if c equal to±1

Verify that the equation of a line passing through the point of intersection of two lines aix+ by +c=0 and a2x + b₂y+c2=0 is of the form

A curve C is composed of 2 line-segments. The first line segment connects theorigin to (3,0), and the second line segment connects (3,0) to (3,3). Find theintegral along curve C

the curve of the quadratic function f: f(x)= -ax2+bx+c is drawn on the cartesian coordinate and the vertex of the curve(3,1) the curve intersects the x-axis twice where a,b,c are constants what is the value of c ?

1. Suppose that, for x ≥ 0, the curve C has equation y = 3x − x√x.(a) Find the coordinates of the x-intercepts of C.(4 marks)(b) Find the coordinates of the stationary point of C and determine whether it isa maximum, a minimum or a point of inflection.(7 marks)(c) Sketch the curve C.

The line integral over C, the arc of the parabola x = y2 from (1,-1) to (1,1)