A) \[4x-3y=\pm \sqrt{20}\]
B) \[4x-3y=\pm \sqrt{12}\]
C) \[4x-3y=\pm \sqrt{2}\]
D) \[4x-3y=\pm 1\]
Correct Answer: A
Solution :
Let the equation of tangent, which is perpendicular to the line\[3x+4y=7\], is\[4x-3y=\lambda \]. Since, it is a tangent to the ellipse. \[\therefore \] \[{{\lambda }^{2}}={{a}^{2}}{{m}^{2}}+{{b}^{2}}\] Here,\[{{a}^{2}}=9,\,\,{{b}^{2}}=4\]and\[m=\frac{4}{3}\] \[\therefore \] \[{{\lambda }^{2}}=9\times {{\left( \frac{4}{3} \right)}^{2}}+4\] \[=16+4\] \[\Rightarrow \] \[{{\lambda }^{2}}=20\] \[\Rightarrow \] \[\lambda =\pm \sqrt{20}\] \[\therefore \]Equation is\[4x-3y=\pm \sqrt{20}\]
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