`P(x , y)` is a variable point on the parabola `y^2=4a x` and `Q(x+c ,y+c)` is another variable point, where `c` is a constant. The locus of the midpoint of `P Q` is an (a)parabola (b) ellipse (c)hyperbola (d) circle

Explanation

`cosA+cosB+2cosC=2`

`cosA+cosB=2(1-cosC)`

`cosA+cosB=4sin^2(C/2)`

`2cos((A+B)/2)cos((A-B)/2)=4cis^2(C/2)`

`cos((A-B)/2)=2sinn(C/2)`

`2cos(C/2)cos((A-B)/2)=4sin(C/2)cos(C/2)`

`2sin((A+B)/2)cos((A-B)/2)=sinC`

`sinA+sinB=2sinC`

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