The equation of latus rectum of parabola is x + y = 8 and the equation of the tangent of the vertex is x +y = 12 and length of the latus rectum is a√2 , then the value of a is

Question

The equation of latus rectum of parabola is x + y = 8 and the equation of the tangent of the vertex is x +y = 12 and length of the latus rectum is a√2 , then the value of a is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

a =|(-8/√1+1)| -|(-12/√1+1)| =(4/√2) Length of latus rectum= 4a =4×(4/√2) =8√2 ⇒ a √2 =8√2 ⇒ a =8

Q. The equation of latus rectum of parabola is $x + y = 8$ and the equation of the tangent of the vertex is $x + y = 12$ and length of the latus rectum is $a 2$ , then the value of a is

$a = ∣ ∣ \frac{- 8}{1 + 1} ∣ ∣ - ∣ ∣ \frac{- 12}{1 + 1} ∣ ∣ = \frac{4}{2}$
Length of latus rectum $= 4 a = 4 \times \frac{4}{2} = 82$
$\Rightarrow a 2 = 82 \Rightarrow a = 8$

Q. The equation of latus rectum of parabola is x+y=8 and the equation of the tangent of the vertex is x+y=12 and length of the latus rectum is a2​ , then the value of a is

a=∣∣​1+1​−8​∣∣​−∣∣​1+1​−12​∣∣​=2​4​ Length of latus rectum=4a=4×2​4​=82​ ⇒a2​=82​⇒a=8

Q. The equation of latus rectum of parabola is $x + y = 8$ and the equation of the tangent of the vertex is $x + y = 12$ and length of the latus rectum is $a 2$ , then the value of a is

$a = ∣ ∣ \frac{- 8}{1 + 1} ∣ ∣ - ∣ ∣ \frac{- 12}{1 + 1} ∣ ∣ = \frac{4}{2}$
Length of latus rectum $= 4 a = 4 \times \frac{4}{2} = 82$
$\Rightarrow a 2 = 82 \Rightarrow a = 8$