12th Grade > Mathematics
INTRODUCTION TO CONICS AND PARABOLA MCQs
Total Questions : 14
| Page 1 of 2 pages
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).
:
D
It is a fundamental concept.The end points of latus rectum of the parabola x2=4ay are(-2a , a) , (2a, a).
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 ) .
:
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 ) .
Answer: Option C. -> 43
:
C
The point (-3,2) will satisfy the equation y2=4ax
⇒ 4 = -12a ⇒4a=−43=43, (Taking positive sign).
:
C
The point (-3,2) will satisfy the equation y2=4ax
⇒ 4 = -12a ⇒4a=−43=43, (Taking positive sign).
Answer: Option D. -> (0, -4)
:
D
a = 4 , vertex = (0,0) , focus = (0,-4) .
:
D
a = 4 , vertex = (0,0) , focus = (0,-4) .
Answer: Option C. -> 20
:
C
Distance between vertex and directrix = a = 5 units.
Therefore , latus rectum = 4a = 20
:
C
Distance between vertex and directrix = a = 5 units.
Therefore , latus rectum = 4a = 20
Answer: Option A. -> 3
:
A
The equation to the pair of tangents is [−y−2(x−2)]2=(1+8)(y2−4x)⇒(−2x−y+4)2=−(y2−4x)
⇒4x2+y2+16−16x−8y+4xy=9y2−36x⇒4x2+4xy−8y2+20x−8y+16=0
∴tanα=2√4+32|4−8|=2×64=3
:
A
The equation to the pair of tangents is [−y−2(x−2)]2=(1+8)(y2−4x)⇒(−2x−y+4)2=−(y2−4x)
⇒4x2+y2+16−16x−8y+4xy=9y2−36x⇒4x2+4xy−8y2+20x−8y+16=0
∴tanα=2√4+32|4−8|=2×64=3
Answer: Option C. -> (4, 0)
:
C
Vertex = (2,0) ⇒ focus is (2+2 ,0) = (4,0).
:
C
Vertex = (2,0) ⇒ focus is (2+2 ,0) = (4,0).
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.
:
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.
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) .
:
D
a = 3 ⇒ abscissa is 4 - 3 = 1 and y2=12,y=±2√3.
Hence points are (1,2√3),(1,−2√3) .
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