Question

Let P (x, y) be the midpoint of the line joining (1, 0) to the point on the curve y^2= (x+1)(x+5) – (x+2)(x+3). The locus of P is symmetric about ?

a). y-axis
b). x=1
c). y=1
d). x-axis
e). (0, 0)

Answer 1

See below.

Explanation:

Note that `y^2=(x + 1) (x + 5) - (x + 2) (x + 3) = x-1`

so the curve is the parabola

`y^2=x-1`

The mid point locus `P(x,y) = 1/2(x+1,y)` is symmetric about the `x` axis

See attached plot.

In red `y^2= x-1` and in blue `P(x,y) = 1/2(x+1,y)`