Prove that graphs of `y=x^2+2a n dy=3x-4` never intersect.

Prove that graphs y=2x-3a n dy=x^2-x never interest.

Sketch the graph of y = (3x)/(x^(2) - 4)

The graph y=2x^3-4x+2a n dy=x^3+2x-1 intersect in exactly 3 distinct points. Then find the slope of the line passing through two of these points.

Consider the graphs of y = Ax^2 and y^2 + 3 = x^2 + 4y , where A is a positive constant and x,y in R .Number of points in which the two graphs intersect, is

Draw the graph of y=x^(2)-3x -4 , find its line of symmetry, vertex, x intercepts

Prove that the locus of the point of intersection of the tangents at the ends of the normal chords of the hyperbola x^2-y^2=a^2 is a^2(y^2-x^2)=4x^2y^2dot

Without sketching the graphs, find whether the graphs of the following functions will intersect the x-axis and if so in how many points. y = x^(2) + x + 2,