A) \[\left( \frac{a}{2},\ \frac{a}{2} \right)\]
B) \[\left( \frac{a}{4},\ \frac{a}{4} \right)\]
C) \[\left( \frac{a}{2},\ \frac{a}{4} \right)\]
D) \[\left( \frac{a}{4},\ \frac{a}{2} \right)\]
Correct Answer: D
Solution :
Parabola is \[{{y}^{2}}=ax\]i.e., \[{{y}^{2}}=4\left( \frac{a}{4} \right)\,x\] .....(i) \[\because \] Let point of contact is \[({{x}_{1}},\,{{y}_{1}})\] \ Equation of tangent is \[y-{{y}_{1}}=\frac{2\left( \frac{a}{4} \right)}{{{y}_{1}}}\,(x-{{x}_{1}})\] Þ \[y=\frac{a}{2{{y}_{1}}}(x)\,-\frac{a{{x}_{1}}}{2{{y}_{1}}}+{{y}_{1}}\] Here, \[m=\frac{a}{2{{y}_{1}}}=\,\tan \,{{45}^{o}}\]\[\Rightarrow \,\]\[\frac{a}{2{{y}_{1}}}=1\] Þ \[{{y}_{1}}=\frac{a}{2}\] From (i), \[{{x}_{1}}=\frac{a}{4}\]. \ Point is \[\left( \frac{a}{4},\,\frac{a}{2} \right)\].
You need to login to perform this action.
You will be redirected in
3 sec
