Find-the-equation-of-tangent-to-the-ellipse-x-2-4y-2-4-which-are-perpendicular-to-the-line-2x-3y-1-merry-X-mas-and-happy-new-year-

Question Number 51151 by peter frank last updated on 24/Dec/18

F i n d t h e e q u a t i o n o f

t a n g e n t t o t h e e l l i p s e

x^{2} + 4 y^{2} = 4 w h i c h a r e

p e r p e n d i c u l a r t o t h e

l i n e 2 x - 3 y = 1

* m e r r y X - m a s a n d h a p p y n e w y e a r *

Answered by tanmay.chaudhury50@gmail.com last updated on 24/Dec/18

3 y = 2 x - 1

y = \frac{2}{3} x - \frac{1}{3}

t a n g e n t y = - \frac{3}{2} x + c

c = \sqrt{a^{2} m^{2} + b^{2}}

\frac{x^{2}}{2^{2}} + \frac{y^{2}}{1^{2}} = 1

c = \sqrt{2^{2} \times \frac{{(- 3)}^{2}}{2^{2}} + 1^{2}} = \sqrt{10}

t a n g e n t i s

y = - \frac{3 x}{2} + \sqrt{10}