Find coordinates of the point on the parabola. Also, find focal distan

1.	Find coordinates of the point on the parabola. Also, find focal distance: 2y2 = 7x whose parameter is -2
Answer» Given equation of the parabola is 2y² = 7x. ⇒ y² = 7/2 x Comparing this equation with y² = 4ax, we get ⇒ 4a = = 7/2 ⇒ a = = 7/8 If t is the parameter of the point P on the parabola, then P(t) = (at² , 2at) i.e., x = at² and y = 2at …..(i) Given, t = -2 Substituting a = 7/8 and t = -2 in (i), we get x = 7/8 (-2)2 and y = 2 (7/8) (-2) x = 7/2 and y = -7/2 The co-ordinates of the point on the parabola are (7/2, -7/2) ∴ Focal distance = x + a = 7/2 + 7/8 = 35/8

Find coordinates of the point on the parabola. Also, find focal distance: 2y2 = 7x whose parameter is -2

Answer»

Given equation of the parabola is 2y² = 7x.

⇒ y² = 7/2 x

Comparing this equation with y² = 4ax, we get

⇒ 4a = = 7/2

⇒ a = = 7/8

If t is the parameter of the point P on the parabola, then

P(t) = (at² , 2at)

i.e., x = at² and y = 2at …..(i)

Given, t = -2

Substituting a = 7/8 and t = -2 in (i), we get

x = 7/8 (-2)2 and y = 2 (7/8) (-2)

x = 7/2 and y = -7/2

The co-ordinates of the point on the parabola are

(7/2, -7/2)

∴ Focal distance = x + a

= 7/2 + 7/8

= 35/8