Question

Let the straight line 5x + 12y = k touches the hyperbola $x^2-9y^2=9$ at the point P. Then

• A. $K=9andP=(-5,\frac{4}{3})$
• B. $K=9andP=(5,\frac{-4}{3})$
• C. $K=-9andP=(-5,\frac{4}{3})$
• D. $K=-9andP=(5,\frac{-4}{3})$

Answer 1

Answer: (B), (D)

The correct options are
B $K=9andP=(5,\frac{-4}{3})$
D $K=-9andP=(5,\frac{-4}{3})$

Equ. of Hyperbola: $\frac{x^2}{9}-y^2=1\Rightarrow a^2=9,b^2=1$
Equ. Of line: $5x+12y=k\Rightarrow l=5,m=12,n=k$
Condition : $a^2{l}^2-b^2{m}^2=n^2\Rightarrow k=\pm 9$
Point of contact : $(\frac{-a^{2}l}{n},\frac{b^{2}m}{n})$