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

The number of tangents to the hyperbola x24−y23=1\frac{x^{2}}{4} - \frac{y^{2}}{3} = 1 through (4, 1) is

A

1

B

2

C

0

D

3

Answer

2

Explanation

Solution

Since x24−y23−1](4,1)=164−13−1>0\left. \ \frac{x^{2}}{4} - \frac{y^{2}}{3} - 1 \right\rbrack_{(4,1)} = \frac{16}{4} - \frac{1}{3} - 1 > 0,

∴ the point (4, 1) lies outside the hyperbola, hence the

number of tangents through (4, 1) is two.