Question

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

Answer 1

Answer: The length of the latus rectum is 8*sqrt2.

Step-by-step explanation:

We know the equation of the line of latus rectum of a parabola passes through the focus of parabola.

The equation of latus rectum and the equation of tangent at the vertex are parallel and distance between these two lines gives focal length.

So,

Using the formula of distance between two parallel lines, we get:

Focal length, a = absolute value of (12-8)/sqrt(1^2+1^2)=4/sqrt2= 2sqrt2

We also know  

Length of the latus rectum= 4*a= 4*2sqrt2= 8*sqrt2

Answer 2

Answer:

Step-by-step explanation: