Question

The angle between the tangents drawn from the origin to the parabola $y^2=4a(x-a)$ is

• A. $90^{\circ }$
• B. $30^{\circ }$
• C. $ta{n}^{-1}\frac{1}{2}$
• D. $45^{\circ }$

Answer 1

Answer: (A)

Given parabola is $y^2=4a(x-a)$
Equation of tangent : $S{S}_1=T^2$
$[y^2-4a(x-a)][y_1^2-4a(x_1-a)]$
$={\left[y{y}_1-4a\left(\frac{x+x_1}{2}-a\right)\right]}^2$
At $x_1=0,y_1=0$, we have
$\left(y^2-4ax+4a^2\right)4a^2={\left(-2ax+4a^2\right)}^2$
$\Rightarrow y^2-4ax+4a^2=x^2+4a^2-4ax\Rightarrow x^2-y^2=0$
$\Rightarrow tan\theta =\frac{2\sqrt{h^2-ab}}{a+b}=\frac{2\sqrt{0-1.\left(-1\right)}}{1+\left(-1\right)}=\infty$
$\Rightarrow \theta =90^{\circ }$