Question

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

Answer 1

Answer:

The measure of length of latus rectum is 20  unit .

Step-by-step explanation:

Given as :

The focus of the parabola = 3 , 4

The equation of tangent is x + y = 7 + 5√2

Let The Latus rectum = L

According to question

Latus rectum = 4 × distance of focus from tangent

∵ distance of focus from tangent = $\dfrac{3 + 5 - 7 -5\sqrt{2}}{\sqrt{1^{2}+1^{2}}}$

or, distance of focus from tangent = $\dfrac{1 -5\sqrt{2}}{\sqrt{2}}$

∴ Latus rectum = 4 × $\dfrac{3 + 5 - 7 -5\sqrt{2}}{\sqrt{1^{2}+1^{2}}}$

Or, L = 20

Hence, The measure of length of latus rectum is 20  unit . Answer