Introduction To Conics And Parabola(11th And 12th > Mathematics ) Questions and Answers
Question 1.
The end points of latus rectum of the parabola x2=4ay are
-
(a,2a) , (2a, -a)
-
(-a,2a) , (2a, a)
-
(a, - 2a) , (2a, a)
-
(-2a , a) , (2a, a)
Explanation:-
Answer: Option D. ->
(-2a , a) , (2a, a)
:
D
It is a fundamental concept. The end points of latus rectum of the parabola x2=4ay are (-2a , a) , (2a, a).
Explanation:-
Answer: Option D. ->
(0, -4)
:
D
a = 4 , vertex = (0,0) , focus = (0,-4) .
Explanation:-
Answer: Option B. ->
(15.25),(15,−25)
:
B
y2=4.15x;a=15 . Focus is (15,0) and co-ordinates of latus rectum are y2=425⇒y=±25
or end points of latus rectum are (15,±25) .
Explanation:-
Answer: Option C. ->
(-4, -2) and (4, -2)
:
C
x2=−8y⇒a=−2. So , focus = (0,-2)
Ends of latus rectum = (4,-2) , (-4,-2) .
Trick: Since the ends of latus rectum lie on parabola , so only points (-4,-2) and (4,-2) satsify the parabola.
Explanation:-
Answer: Option D. ->
None of these
:
D
a = 3 ⇒ abscissa is 4 - 3 = 1 and y2=12,y=±2√3.
Hence points are (1,2√3),(1,−2√3) .
Explanation:-
Answer: Option A. ->
(0, 0), (4, 12)
:
A
y1=3x1 . According to given condition 9x21=36x1
⇒x1=4,0⇒y1=12,0
Hence the points are (0,0) and (4,12).
Explanation:-
Answer: Option B. ->
3√2
:
B
Distance between focus and directrix is
= ∣∣∣3−4−2√2∣∣∣=±3√2
Hence latus rectum = 3√2
( Since latus rectum is two times the distance between focus and directrix ) .
Explanation:-
Answer: Option A. ->
9y2=4ax
:
A
Required locus is (3y)2 = 4ax
⇒ 9y2=4ax .
Explanation:-
Answer: Option B. ->
8
:
B
Let the equation of parabola is x2=4ay, but a = 4−2=−2.Then equation is x2=−8y and latus rectum = 4a = 8
Explanation:-
Answer: Option C. ->
43
:
C
The point (-3,2) will satisfy the equation y2=4ax
⇒ 4 = -12a ⇒4a=−43=43, (Taking positive sign).