Question

From Point p(2,3) two tangents PA and PB are drawn to the hyperbola x ^ 2 - y ^ 2 - 4x + 4y + 16 = 0 The equation of line AB​

Answer 1

Answer:

It is given that tangents to the hyperbola

9

x

2

−

36

y

2

=1 at point P and Q intersect at T(0,3)

The equation of tangent at a point (x

1

,y

1

) is given by:

9

xx

1

−

36

yy

1

=1

Thus, the above equation of line passes through (0,3)

Substituting this in the above equation, we get

y

1

=−12

9

x

2

−4=1

(x

1

)

2

=45

Or, (x

1

)=±3

5

Thus, the points P and Q are (3

5

,−12) and (−3

5

,−12)

Now, using the area of the triangle where points of the triangle are P,Q and T is

A=

2

1

∣

∣

∣

∣

∣

∣

∣

∣

3

5

−3

5

0

−12

−12

3

1

1

1

∣

∣

∣

∣

∣

∣

∣

∣

Solving the above determinant we get A=45

5