Question

The points of contact $Q$ and $R$ of tangent from the point $P(2,3)$ on the parabola $y^2=4x$ are

• A. $(9,6)$ and $(1,2)$
• B. $(1,2)$ and $(4,4)$
• C. $(4,4)$ and $(9,6)$
• D. $(9,6)$ and $(\frac{1}{4},1)$

Answer 1

The correct option is B $(1,2)$ and $(4,4)$

Slope of tangent line $(y^2=4x)$: $2y\frac{dy}{dx}=4$

$\frac{dy}{dx}=2_{/y}$

Equation of tangent $P(2,3)$ $\Rightarrow y-y_1=M(x-x_1)$

$y-3=\frac{2}{y}(x-2)$

$\Rightarrow y^2-3y=2x-4$ $\{$ we know $y^2=y,x=y_{/4}^2$ $\}$

$\Rightarrow y^2-3y=2\left(\frac{y^2}{4}\right)-4$

$\Rightarrow y^2-\frac{y^2}{2}-3y+4=0$

$\Rightarrow y^2-6y+8=0$

$\Rightarrow y^2-4y-2y+8=0$

$\Rightarrow y(y-4)-2(y-4)$

$\Rightarrow y_1=2,4$ $\left\{\right(x=y_{/4}^2\left)\right\}$

$\therefore$ Points are $(1,2)$ & $(4,4)$.