The number of tangents to the hyperbola x2-4-y2-3-1 through 1-4

Position of point (1,4) w.r.t. hyperbola x^24 y^23=1 is S_1= 14 163 1 ⇒ S_1 lt;0 ∴ The point (1,4) lies outside the hyperbola Hence the number of tangen ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Position of a Point W.R.T Hyperbola

The number of...

Question

The number of tangents to the hyperbola $\frac{x^{2}}{4} - \frac{y^{2}}{3} = 1$ through $(1, 4)$ is

Open in App

Solution

Position of point $(1, 4)$ w.r.t. hyperbola
$\frac{x^{2}}{4} - \frac{y^{2}}{3} = 1$ is
$S_{1} = \frac{1}{4} - \frac{16}{3} - 1 \Rightarrow S_{1} < 0$
$∴$ The point $(1, 4)$ lies outside the hyperbola
Hence the number of tangents that can be drawn from $(1, 4)$ is $2.$

Suggest Corrections

Similar questions

Q. The slope of the tangent to the hyperbola

\frac{x^{2}}{25} - \frac{y^{2}}{16} = 1

which passes through the point

(1, 4)

Q. Find the common tangent to the hyperbola

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

and an ellipse

\frac{x^{2}}{4} + \frac{y^{2}}{3} = 1

Q. The total number of tangents to the hyperbola

\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1

that are perpendicular to the line

5 x + 2 y - 3 = 0

Q. The total number of tangents to the hyperbola

\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1

that are perpendicular to the line

5 x + 2 y - 3 = 0

Q. Tangents are drawn from the points on a tangent of the hyperbola

x^{2} - y^{2} = a^{2}

to the parabola

y^{2} = 4 a x

. If all the chords of contact pass through a fixed point

Q

, then the locus of the point

Q

for different tangents on the hyperbola is

Join BYJU'S Learning Program

The number of tangents to the hyperbola x24−y23=1 through (1,4) is

Position of point (1,4) w.r.t. hyperbola x24−y23=1 is S1=14−163−1⇒S1<0 ∴ The point (1,4) lies outside the hyperbola Hence the number of tangents that can be drawn from (1,4) is 2.

The number of tangents to the hyperbola $\frac{x^{2}}{4} - \frac{y^{2}}{3} = 1$ through $(1, 4)$ is

Position of point $(1, 4)$ w.r.t. hyperbola
$\frac{x^{2}}{4} - \frac{y^{2}}{3} = 1$ is
$S_{1} = \frac{1}{4} - \frac{16}{3} - 1 \Rightarrow S_{1} < 0$
$∴$ The point $(1, 4)$ lies outside the hyperbola
Hence the number of tangents that can be drawn from $(1, 4)$ is $2.$