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

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10-2. Parabola, Ellipse, Hyperbola

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

A

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

B

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

C

$y = 4,\;x + y = 3$

D

$y = - 4,\;x - y = 3$

Solution

(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 $x + y = 5$.

Standard 11

Mathematics

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