Question

The two curves $y^2$ = 4x and $x^2+y^2$ – 6x + 1 = 0 at the point (1, 2):

• A. intersect orthogonally
• B. intersect at an angle $\frac{\pi }{3}$
• C. touch each other
• D. intersect at an angle $\frac{\pi }{6}$

Answer 1

The correct option is C touch each other

$y^2=4x$
$\Rightarrow 2y\frac{dy}{dx}=4$
$\Rightarrow \frac{dy}{dx}=\frac{2}{y}$
$\therefore M_1=1$
$x^2+y^2-6x+1=0$
$\Rightarrow 2x+2y.\frac{dy}{dx}-6=0$
$\Rightarrow \frac{dy}{dx}=\frac{3-x}{y}$
$\therefore M_2={\left(\frac{dy}{dx}\right)}_{1,2}=1$
$\therefore M_1=M_2\Rightarrow$ curves touch each other