Find the latus rectum $&$ equation of parabola whose vertex is origin $&$ direct is $x + y = 2.$

Open in App

Solution

$x + y = 2$ is directrix of parabola

vertex is $A (0, 0)$

latus rectum $\Rightarrow 4 a \Rightarrow 4 \sqrt{2} .$

eq. of parabola $\Rightarrow$

${(\frac{x - y}{\sqrt{2}})}^{2} = 4 \sqrt{2} [\frac{x + y}{\sqrt{2}}]$

$(x - y)^{2} = 8 x + y$

$\Rightarrow x^{2} - 2 x y + y^{2} - 8 x - 8 y = 0$

Suggest Corrections

Similar questions

Latus rectum of the parabola whose focus is (3,4) and whose tangent at vertex has the equation x + y = 7 + 5√2 is ?

V

L

x^{2} = 2 y + 4 x - 4

V

L / 2

2

x + y - 2 = 0

x - y + 4 = 0

(1, - 1)

(2, 1) .

(2, - 3)

8

Join BYJU'S Learning Program