Number of real tangents, which can be drawn from the point $(4, 3)$ to the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1,$ is

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Solution

Given point $P = (4, 3) .$
Ellipse $S \equiv \frac{x^{2}}{16} + \frac{y^{2}}{9} - 1 = 0$
$∵ S_{1} = \frac{16}{16} + \frac{9}{9} - 1 = 1 > 0$
$\Rightarrow$ Point $P$ lies outside the ellipse.

So, two real tangents are possible

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Number of real tangents, which can be drawn from the point (4,3) to the ellipse x216+y29=1, is

Given point P=(4,3). Ellipse S≡x216+y29−1=0 ∵S1=1616+99−1=1>0 ⇒ Point P lies outside the ellipse. So, two real tangents are possible

Number of real tangents, which can be drawn from the point $(4, 3)$ to the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1,$ is

Given point $P = (4, 3) .$
Ellipse $S \equiv \frac{x^{2}}{16} + \frac{y^{2}}{9} - 1 = 0$
$∵ S_{1} = \frac{16}{16} + \frac{9}{9} - 1 = 1 > 0$
$\Rightarrow$ Point $P$ lies outside the ellipse.

So, two real tangents are possible