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

Answer

4

Explanation

We have `y=Ax^(2),y^(2)+3=x^(2)+4y,Agt0`
Now, `y^(2)-4y=x^(2)-3`
`"or "(y-2)^(2)=x^(2)+1`
`"or "(-2)^(2)-x^(2)=1`
If x = 0, then
`y-2 =1 or -1`
Hence, the two graphs of `y=Ax^(2)(Agt0)` and the hyperbola `(y-2)^(2)-x^(2)=1` are as shown which intersect at four points.