Equation of tangents drawn at ends of major axis of ellipse 9{x^2} + 5{y^2} - 30y = 0 , are

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10-2. Parabola, Ellipse, Hyperbola

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The equation of the tangents drawn at the ends of the major axis of the ellipse $9{x^2} + 5{y^2} - 30y = 0$, are

A

$y = \pm 3$

B

$x = \pm \sqrt 5 $

C

$y = 0,\;y = 6$

D

None of these

Solution

(c) Change the equation $9{x^2} + 5{y^2} – 30y = 0$ in standard form $9{x^2} + 5({y^2} – 6y) = 0$

==> $9{x^2} + 5({y^2} – 6y + 9) = 45$

==> $\frac{{{x^2}}}{5} + \frac{{{{(y – 3)}^2}}}{9} = 1$

$\because {a^2} < {b^2},$ so axis of ellipse on $y$ – axis.

At $y$ axis, put $x = 0$, so we can obtained vertex.

Then $0 + 5{y^2} – 30y = 0$

$y = 0,\,\,y = 6$

Therefore, tangents of vertex $y = 0,\,\,\,y = 6$.

Standard 11

Mathematics

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