A) \[5(y-3)=2\left( x-\frac{\sqrt{117}}{2} \right)\]
B) \[2x-5y+10-2\sqrt{18}=0\]
C) \[2x-5y-10-2\sqrt{18}=0\]
D) None of the above
Correct Answer: D
Solution :
\[4{{x}^{2}}-9{{y}^{2}}=36\] On differentiating w.r.t.\[x,\]we get \[\Rightarrow \] \[8x-18y\frac{dy}{dx}=0\] \[\Rightarrow \] \[\frac{dy}{dx}=\frac{4x}{9y}\] Slope of the tangent\[=\frac{4x}{9y}\] \[\therefore \]For this tangent to be perpendicular to the straight line\[5x+2y-10=0,\] we must have \[\frac{4x}{9y}\times \frac{5}{-2}=-1\] \[\Rightarrow \] \[y=\frac{10x}{9}\] Putting this value of y in\[4{{x}^{2}}-9{{y}^{2}}=36,\]we get \[-64{{x}^{2}}=324,\]which does not have real roots. Hence, at no points on the given curve can the tangent be perpendicular to given line.You need to login to perform this action.
You will be redirected in
3 sec