Consider the parabola y2
= 16x.
(i) Length of the latus rectum of the parabola is _______.
(a) 4 (b) 16 (c) 8 (d) 32 (1)
(ii) Write the co-ordinates of the focus and equation of the directrix of the above
parabola.
Answers
Answer:
Given equation can be rewritten as
(x−1)
2
+(y−3)
2
=(
13
5x−12y+17
)
2
⇒SP=PM
Here, focus is (1,3), directrix
5x−12y+17=0
∴ the distance of the focus from the directrix
=
∣
∣
∣
∣
∣
25+144
5−36+17
∣
∣
∣
∣
∣
=
13
14
=2a
∴ Latusrectum =2×
13
14
=
13
28
Given : parabola y² = 16x
To Find : Length of the latus rectum of the parabola
(a) 4 (b) 16 (c) 8 (d) 32
the co-ordinates of the focus and equation of the directrix
Solution:
y² = 16x HORIZONATAL PARABOLA origin
y² = 4(4)x
Comparing with
y² = 4px Standard equation of horizontal parabola ( origin)
p = 4
Length of Latus rectum = 4p
= 4(4) = 16
Length of the latus rectum of the parabola is 16
Correct option is option b ) 16
Focus = ( p , 0) = ( 4 , 0)
Equation of the directrix
x = - p
x = - 4
or x + 4 = 0
Learn More:
नाभि के निर्देशांक, परवलय का अक्ष, नियता का समीकरण और नाभिलंब जीवा की लंबाई ज्ञात कीजिए:
brainly.in/question/15777564
नाभि के निर्देशांक, परवलय का अक्ष, नियता का समीकरण और नाभिलंब जीवा की लंबाई ज्ञात कीजिए:
brainly.in/question/15777567
