TS EAMCET 2017 Code A Solved Paper

The equation of normal to the given hyperbola is
‌‌

a2x

x1

+‌‌

b2y

y1

=a2−b2
‌‌

9x

x1

+‌‌

4y

y1

=9+4
‌‌

9x

x1

+‌‌

4y

y1

=13
As the line x+y=k is normal to the given hyperbola therefore,
‌‌

‌‌ 9 x1

1

=‌‌

‌‌ 4 y1

1

=‌‌

13

k

‌‌

9

x1

=‌‌

4

y1

=‌‌

13

k

From the above equation, we get
x1=‌‌

9k

13

y1=‌‌

4k

13

since (x1,y1) lie on the hyperbola, therefore
‌‌

(‌‌ 9k 13 )2

9

−‌‌

(‌‌ 4k 13 )2

4

=1
‌‌

9k2

169

−‌‌

4k2

169

=1
5k2=169
k=±‌‌

13

√5