Question

Equation of the two tangents drawn from (1,4) to the parabole $y^2=12x$ are

• A. x -y + 3 = 0,3x - y +1 =0
• B. x - y + 1 = 0, x -2y + 4 = 0
• C. x + y -2 = 0, x - y = 3
• D. x + y -1 =0, x + 2y +4 =0

Answer 1

The correct option is A x -y + 3 = 0,3x - y +1 =0

Equation of tangent to parabola: $y=mx+a/m$

(m$=$ slope of tangent)

Here $a=3$

$\Rightarrow my=m^{2}x+3$

$\Rightarrow m^2\left(1\right)-4m+3=0$

$\Rightarrow m^2-3m-m+3=0$

$\Rightarrow m(m-3)-1(m-3)=0$

$\Rightarrow (m-1)(m-3)=0$

$\Rightarrow m=1$ or $m=3$

$\Rightarrow$ Equation $y=x+3$ or $y=3x+1$

$\Rightarrow \left(A\right)$.