Question

The equation of a tangent to the hyperbola $16 x^{2}-25 y^{2}-96 x+100 y-356=0$ which makes an angle $45^{\circ}$ with its transverse axis is

• A. x - y + 2 = 0
• B. x - y + 4 = 0
• C. x + y + 2 = 0
• D. x + y + 4 = 0

Answer 1

Answer: (A)

Given equation of hyperbola
$16 x^{2}-25 y^{2}-96 x+100 y-356=0$
$\Rightarrow \frac{(x-3)^{2}}{25}-\frac{(y-2)^{2}}{16}=1$ ...(i)
Now equation of tangent to the hyperbola (i) having slope $'1'$ is
$y-2=1(x-3)+\sqrt{25(1)-16}$
$\Rightarrow y-2=x-3+3$
$y-2=x-3+3$ or $y-2=x-3-3$
or $x-y-4=0$
$\Rightarrow x-y+2=0$