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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 x24y23=1\frac{x^{2}}{4} - \frac{y^{2}}{3} = 1

through (4, 1) is

A

1

B

2

C

0

D

3

Answer

0

Explanation

Solution

Since the point (4, 1) lies inside the hyperbola [164131>0]\left\lbrack \because\frac{16}{4} - \frac{1}{3} - 1 > 0 \right\rbrack; \therefore Number of tangents through (4, 1) is 0.