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

Open in App

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

Suggest Corrections

Similar questions

How many real tangents can be drawn from the point (4,3) to the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1.$ Find the equation of these tangents & angle between them.

Q. 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,

How many real tangents can be drawn from the point $(4, 3)$
to hyperbola $\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1$ Find the equation of these tangents & angle between them.

Q. Number of points on the ellipse

\frac{x^{2}}{50} + \frac{y^{2}}{20} = 1

from which prependicular of tangents are drawn to the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

Q. Number of points on the ellipse

\frac{x^{2}}{50} + \frac{y^{2}}{20} = 1

from which pair of perpendicular tangents are drawn to the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

Join BYJU'S Learning Program

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