The equation of tangents to the hyperbola 3x² - 2y² = 6, which is perpendicular to the line x - 3y = 3, are

Correct Answer is : y = - 3x ± 15{15}15

Correct Answer is : y = - 3x ± 15{15}15

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VITEEE 2015 Paper

Section: Mathematics

Question : 108 of 120

Marks: +1, -0

3x^2 - 2y^2

Solution:

Equation of hyperbola is

3x^2 - 2y^2

= 6

⇒

\frac{x^2}{2}-\frac{y^2}{3}

= 1

So ,

a^2

= 2 and

b^2

= 3

Given, equation of line is x - 3y = 3.

∴ Slope of given line =

\frac{1}{3}

∴ Slope of line perpendicular to given line, m = -3

The equation of tangents are

y = mx ±

\sqrt{a^2m^2-b^2}

= - 3x ±

\sqrt{2\times 9-3}

= - 3x ±

\sqrt{18-3}

= - 3x ±

\sqrt{15}

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