Jee Main 2024 31 01 2024 Shift2 - Question10
Question 10
The line passes through the centre of circle $x^{2}+y^{2}-16 x-4 y=0$, it interacts with the positive coordinate axis at $A \& B$. Then find the minimum value of $O A+O B$, where $O$ is origin.
20
18
12
24
Show Answer
Answer: (1)
Solution:
$(y-2)=m(x-8)$
$$ \begin{alignedat} & \Rightarrow \quad x \text {-intercept } \\ & \Rightarrow \quad\left(\frac{-2}{m}+8\right) \\ & \Rightarrow y\text{-intercept } \\ & \Rightarrow(-8 m+2) \\ & \Rightarrow O A+O B=\frac{-2}{m^{2}}+8-8 m+2 \\ & f^{\prime}(m)=\frac{2}{m^{2}}-8=0 \\ & \Rightarrow m^{2}=\frac{1}{4} \end{aligned} $$
$$ \begin{alignedat} & \Rightarrow m=\frac{-1}{2} \\ & \Rightarrow \quad f\left(\frac{-1}{2}\right)=18 \\ & \Rightarrow \text { Minimum }=18 \end{aligned} $$
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