A) \[{{(y+3)}^{2}}\]\[~=24(x+3)\]
B) \[{{(y+3)}^{2}}=-24(x+3)\]
C) \[{{(y-3)}^{2}}=-24(x-3)\]
D) \[{{(y-3)}^{2}}=24(x-3)\]
Correct Answer: C
Solution :
Given, vertex \[(h,\text{ }k]=(3,3)\] and focus \[(a+h,k)=(-3,3)\] \[\Rightarrow \] \[a+h=-3\] \[\Rightarrow \] \[a=-3-h\] \[\Rightarrow \] \[=-3-3=-6\] We know that, if y-coordinate of vertex and focus is same, then axis of parabola will be parallel to\[x-\]axis. \[\therefore \] \[{{(y-k)}^{2}}=4a(x-h)\] \[\Rightarrow \] \[{{(y-3)}^{2}}=4(-6)(x-3)\] \[\Rightarrow \] \[{{(y-3)}^{2}}=24(x-3)\]
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