Question

find the coordinates of focus equation of directrix and length of latus rectum of the parabola y square = 10x​

Answer 1

Given :-

• The parabola y² = 10x

To Find :-

• Coordinates of Focus

• Equation of directrix

• Length of Latus Rectum

Formula Used :-

If the equation of Parabola is y² = 4ax, then

• Coordinates of Focus = (a , 0)

• Equation of directrix, x + a = 0

• Length of Latus Rectum = 4a

Solution :-

Given equation of Parabola is y² = 10

On comparing with y² = 4ax, we get

⇛ 4a = 10

$\therefore \: \sf \: a \: = \: \dfrac{5}{2}$

Now,

$\bf \: 1. \: \: Focus = (a, 0) \: \sf \: = \: \bigg( \dfrac{5}{2}, 0 \bigg)$

$\bf \: 2. \: \: Equation \: of \: directrix : x + a = 0$

$\sf \: x + \dfrac{5}{2} = 0$

$\therefore \: \: \bf \: 2x + 5 = 0$

$\bf \: 3. \: \: Length \: of \: Latus \: Rectum= \sf 4a = 4 \times \dfrac{5}{2} = 10$

Additional Information :-

If the equation of Parabola is y² = - 4ax, then

• Coordinates of Focus = (- a , 0)

• Equation of directrix, x - a = 0

• Length of Latus Rectum = 4a

If the equation of Parabola is x² = 4ay, then

• Coordinates of Focus = (0 , a)

• Equation of directrix, y + a = 0

• Length of Latus Rectum = 4a

If the equation of Parabola is x² = - 4ay, then

Coordinates of Focus = (0 , - a)

Equation of directrix, y - a = 0

Length of Latus Rectum = 4a