Question

Question 5 Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y^2 = 10x

Class X1 - Maths -Conic Sections Page 246

Answer 1

concept : if equation of parabola is in the form of y² = 4ax , then
Focus = ( a, 0)
axis of parabola = X - axis
equation of direcrix , x = -a
Length of latusrectum = 4a

Here, equation of parabola
y² = 10x
y² = 4( 10/4)x => y² = 4( 5/2)x
on comparing given equation with equation
y² = 4ax, we get a = 5/2

now, co-ordinate of focus ( a, 0) = ( 5/2, 0)
axis of parabola = X - axis
Directrix , x = -a = -5/2 => x = -5/2
Length of latusrectum = 4a = 4 × 5/2 = 10