First slide

Tangents and normals

Question

For which of the following curves $x + \sqrt{3} y = 2 \sqrt{3}$ , the line is the tangent at the point $(\frac{3 \sqrt{3}}{2}, \frac{1}{2}) ?$

Moderate

A

$x^{2} + y^{2} = 7$
B

$x^{2} + 9 y^{2} = 9$
C

$y^{2} = \frac{1}{6 \sqrt{3}} x$
D

$2 x^{2} - 18 y^{2} = 9$

Solution

$\frac{d y}{d x} = - \frac{1}{\sqrt{3}}$ and passes through $(\frac{3 \sqrt{3}}{2}, \frac{1}{2})$

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