Your initial formula was correct, however, you made a few mistakes in the working.
(you forgot to multiply 4 to x²) =
(you added the 4y, instead of subtracting)
Divide everything by 3 to get the answer required
Part B is relatively straight forward. Substitute point Q into the equation of the locus and check if equality holds (it should)
Then simply find the gradient between two points you already know (B and Q) and then use the point gradient formula.
You didn't "carry the 4."Given: points
Point moves such that the ratio of .
(a) Show that the equation of locus is: .
. . .
. . . .
. . . . . .
Substitute into:(b) Show that point is a point of the locus
The slope of is: .(c) Find the equation of straiggt line
The equation of the line through with slope is: