A) 0
B) 1
C) 2
D) 3
Correct Answer: A
Solution :
Let \[y=mx+c\] is the variable chord which is subtending right angle at the vertex of parabola hence equation of pair of straight lines OP and OQ can be given by making a homogeneous second degree equation with the help of parabola and chord as follows |
\[{{y}^{2}}-4ax\left( \frac{y-mx}{c} \right)=0\] |
for subtend \[90{}^\circ \] at vertex \[1+\frac{4am}{c}=0\] |
\[\Rightarrow \] \[c=-\,4\,\,am\] |
\[\Rightarrow \] equation of chord is |
\[y=m\,(x-4a)\] |
which is always passing through (4a, 0) |
Let point of intersection of tangents at the extremities is \[({{x}_{1}},\,\,{{y}_{1}})\] hence equation of chord of contact is |
\[y\,\,{{y}_{1}}=2a\,(x+{{x}_{1}})\] |
which is passing through (4a, 0) |
\[\Rightarrow \] \[{{x}_{1}}+4a=0\] |
\[\Rightarrow \] \[x+4a=0\] is the required locus. |
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