Question

Consider a parabola having $(1,3)$ as its focus and touching both the co-ordinate axes. then

• A. $y+3 x=0$ is directrix of the parabola
• B. $y+3 x=1$ is tangent at vertex to parabola
• C. length of latus rectum of parabola is 6
• D. $x^2+9 y^2-6 x y-20 x-60 y+100=0$ is the equation of parabola

Answer 1

Answer: (A), (D)

Equation of tangent at vertex is $\frac{x}{1}+\frac{y}{3}=1$
$\Rightarrow 3 x + y =1$
Equation of directrix is $3 x+y=0$
$\Rightarrow \left(\frac{3 x+y}{\sqrt{10}}\right)^2=(x-1)^2+(y-3)^2 $
$\Rightarrow x^2+9 y^2-6 x y-20 x-60 y+100=0$