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

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) x2+9 y2-6 x y-20 x-60 y+100=0 is the equation of parabola

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/4e1dbe81bebe64f3afe607560f419c57-.png" /> Equation of tangent at vertex is (x/1)+(y/3)=1 ⇒ 3 x + y =1 Equation of directrix is 3 x+y=0 ⇒ ((3 x+y/√10))2=(x-1)2+(y-3)2 ⇒ x2+9 y2-6 x y-20 x-60 y+100=0

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

$y + 3 x = 0$ is directrix of the parabola

$y + 3 x = 1$ is tangent at vertex to parabola

length of latus rectum of parabola is 6

$x^{2} + 9 y^{2} - 6 x y - 20 x - 60 y + 100 = 0$ is the equation of parabola

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

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

y+3x=0 is directrix of the parabola

y+3x=1 is tangent at vertex to parabola