A) 12
B) 8
C) 24
D) 32
Correct Answer: C
Solution :
Equation of tangent with slope \[=\frac{-3}{4}\] \[y=\frac{-3}{4}x+C\] Now, \[C=\sqrt{32\times {{\left( \frac{-3}{4} \right)}^{2}}+18}=\sqrt{18+18}=6\] (Using condition of tangency) \[\therefore \]\[y=\frac{-3}{4}x+6\Rightarrow 3x+4y=24\] It meets the coordinate axes in A and B. So, A(8, 0) and B(0, 6). Hence, required area of \[\Delta AOB=\frac{1}{2}(8)(6)=24\]You need to login to perform this action.
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