A) Any straight line through the vertex
B) Any straight line through the focus
C) Any straight line parallel to the axis
D) Another parabola
Correct Answer: C
Solution :
Let \[y=mx+c\]is chord and c is variable \[\Rightarrow x=\left( \frac{y-c}{m} \right)\] by \[{{y}^{2}}=4ax\] For getting points of intersection, \[{{y}^{2}}=4a\left( \frac{y-c}{m} \right)\Rightarrow {{y}^{2}}-\frac{4ay}{m}+\frac{4ac}{m}=0\] Þ \[{{y}_{1}}+{{y}_{2}}=\frac{4a}{m}\Rightarrow \frac{{{y}_{1}}+{{y}_{2}}}{2}=\frac{2a}{m}\] which is a constant; independent to c.
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