Proof of locus of projectile
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Since we have(x−0)2+{y−(−1)}2=|y−1|2,(x−0)2+{y−(−1)}2=|y−1|2,we havex2=4⋅(−1)⋅y.x2=4⋅(−1)⋅y.The vertex is (0,0)(0,0), the axis of symmetry is x=0x=0, the focus is (0,−1)(0,−1), the directrix is y=−(−1)y=−(−1).
sahilsharma2000:
This locus is for any situation where you shoot or throw something at an angle into the air. Things like throwing a tennis ball to a friend, or shooting a gun, or throwing a javelin. The shape of the locus for a situation like this is a parabola, like this one for a thrown cricket ball:
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