For which of the following curves, the line x+√3y=2√3 is the tangent at the point (3√32,12…

Question

For which of the following curves, the line $x+\sqrt3y=2\sqrt3$ is the tangent at the point $\left(\dfrac{3\sqrt3}2,\dfrac12\right)$?

Accepted Answer

Check D: $\left(\frac{3\sqrt3}2\right)^2+9\left(\frac12\right)^2=\frac{27}4+\frac94=9$ , point lies on the curve.

Tangent to $x^2+9y^2=9$ at $(x_0,y_0)$: $xx_0+9yy_0=9$. At the given point: $\frac{3\sqrt3}2x+\frac92y=9\Rightarrow x+\sqrt3y=2\sqrt3$ --- matches exactly.

Solutions · 1