A) \[x-2y+8=0\]
B) \[x+2y+8=0\]
C) \[2x-y-24=0\]
D) \[2x+y-24=0\]
Correct Answer: A
Solution :
Given parabola is \[{{y}^{2}}=8x\] One end of the focal chord is \[\left( \frac{1}{2},-2 \right)\] Let \[\left( \frac{1}{2},-2 \right)=\left( 2t_{1}^{2},\,\,2a{{t}_{1}} \right)\,\,\,\,\,\,\,\,\,\,\Rightarrow {{t}_{1}}=-\frac{1}{2}\] As \[{{t}_{2}}=-\frac{1}{{{t}_{1}}}\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,\,{{t}_{2}}=2\] So, coordinates of the other end are \[(8,\,\,8)\] equation of tangent at \[(8,\,\,8)\] is \[y(8)=4(x+8)\] \[\Rightarrow \,\,\,\,2y=x+8\]
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