The equations of the tangents of the ellipse 9 x^2 + 16 y^2 = 144… - Vidyadip

MCQ

The equations of the tangents of the ellipse $9{x^2} + 16{y^2} = 144$ which passes through the point $(2, 3)$ is

✓
$y = 3,\;x + y = 5$
B
$y = - 3,\;x - y = 5$
C
$y = 4,\;x + y = 3$
D
$y = - 4,\;x - y = 3$

✓

Answer

Correct option: A.

$y = 3,\;x + y = 5$

a
(a) The tangent will be $y - 3 = m(x - 2)$ ==> $y - mx = 3 - 2m.$

But it is tangent to the given ellipse, therefore $m = 0,\, - 1$.

Hence tangents are $y = 3$ and $x + y = 5$.

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