Question
The distance of the point '
' on the ellipse 
from a focus is –
- a (e + cos )
- a (e – cos )
- a (1 + e cos )
- a (1 + 2e cos )
)
)
)
)
Hint:
use the general form of points on a ellipse and find the distance between the focus and the point sing the distance formula.
The correct answer is: a (1 + e cos )
a (1 + e cos )
in an ellipse,
x = acos(theta)
y = b sin(theta)
focus = (±ae,0)
distance = √(ae-acos(theta))2+(bsin(theta))2
b= a√1-e2
=> a√((e2+2ecos(theta) + 1-e2sin2(theta))
=> a√(1+ecos(theta)2
= a(1+cos(theta))
an ellipse has 2 focii at (ae,0 ) and (-ae,0) when the center is (0,0) and the ellipse has the x axis as its major axis. an ellipse is defined as the locus of a point whose sum of the distances from 2 fixed points (focii) is constant.
Related Questions to study
At 
will be [Assume that the concentration of hydroquinone and quinine is (1M)]
At will be [Assume that the concentration of hydroquinone and quinine is (1M)]
Statement-I : If a, b, c are three positive numbers in G.P., then 
Statement-II : (A.M.) (H.M.) = (G.M.)2 is true for any set of positive numbers.
The relation between AM, GM and HM of a sequence states that (AM)(HM)=GM2
Statement-I : If a, b, c are three positive numbers in G.P., then
Statement-II : (A.M.) (H.M.) = (G.M.)2 is true for any set of positive numbers.
The relation between AM, GM and HM of a sequence states that (AM)(HM)=GM2
Statement-I : If x2y3 = 6(x, y > 0), then the least value of 3x + 4y is 10
Statement-II : If m1, m2 
N, a1, a2 > 0 then 
and equality holds when a1 = a2.
the AM GM rule is valid for any set of natural numbers, i.e., numbers > 0.
Statement-I : If x2y3 = 6(x, y > 0), then the least value of 3x + 4y is 10
Statement-II : If m1, m2 N, a1, a2 > 0 then and equality holds when a1 = a2.
the AM GM rule is valid for any set of natural numbers, i.e., numbers > 0.
Statement-I : If a, b, c are three distinct positive number in H.P., then 
Statement-II : Sum of any number and it's reciprocal is always greater than or equal to 2.
when some numbers are in HP, then their reciprocals are in AP.
Statement-I : If a, b, c are three distinct positive number in H.P., then
Statement-II : Sum of any number and it's reciprocal is always greater than or equal to 2.
when some numbers are in HP, then their reciprocals are in AP.
Statement-I : In any ΔABC, maximum value of r1 + r2 + r3 =9R/2.
Statement-II : In any ΔABC, R ≥ 2r.
Statement-I : In any ΔABC, maximum value of r1 + r2 + r3 =9R/2.
Statement-II : In any ΔABC, R ≥ 2r.
Statement-I : If 27 abc ≥ (a + b + c)3 and 3a + 4b + 5c = 12 then 
where a, b, c are positive real numbers.
Statement-II : For positive real numbers A.M. ≥ G.M.
a,b,c are positive real numbers
=> AM>= GM can be applied to these numbers
for real and positive numbers, we can use the property AM>=GM
Statement-I : If 27 abc ≥ (a + b + c)3 and 3a + 4b + 5c = 12 then where a, b, c are positive real numbers.
Statement-II : For positive real numbers A.M. ≥ G.M.
a,b,c are positive real numbers
=> AM>= GM can be applied to these numbers
for real and positive numbers, we can use the property AM>=GM
Statement-I : Minimum value of 
Statement-II : The least value of a sin q + b cosq is 
Statement-I : Minimum value of
Statement-II : The least value of a sin q + b cosq is
At point of intersection of the two curves shown, the conc. of B is given by …….. For,
:
At point of intersection of the two curves shown, the conc. of B is given by …….. For,:
Following is the graph between log 
and log a (a 
initial concentration) for a given reaction at 27oC. Hence, order is
Following is the graph between log and log a (a initial concentration) for a given reaction at 27oC. Hence, order is
Statement-I : Circumradius and inradius of a triangle can not be 12 and 8 respectively.
Statement-II : Circumradius ≥ 2 (inradius)
The circumradius of a cyclic polygon is a radius of the circle inside which the polygon can be inscribed
inradius is the radius of the circle inscribed inside a polygon.
Statement-I : Circumradius and inradius of a triangle can not be 12 and 8 respectively.
Statement-II : Circumradius ≥ 2 (inradius)
The circumradius of a cyclic polygon is a radius of the circle inside which the polygon can be inscribed
inradius is the radius of the circle inscribed inside a polygon.
Statement-I : For n N, 2n > 1 + n 
Statement-II : G.M. > H.M. and (AM) (HM) = (GM)2
for real and positive numbers, we can use the property AM>=GM
the statement 2 doesn't have any connection with statement 1
Statement-I : For n N, 2n > 1 + n
Statement-II : G.M. > H.M. and (AM) (HM) = (GM)2
for real and positive numbers, we can use the property AM>=GM
the statement 2 doesn't have any connection with statement 1
Statement-I : 1, 2, 4, 8, ......... is a G.P., 4, 8, 16, 32 is a G.P. and 1 + 4, 2 + 8, 4 + 16, 8 + 32, ....... is also a G.P.
Statement-II : Let general term of a G.P. (with positive terms) with common ratio r be Tk + 1 and general term of another G.P. (with positive terms) with common ratio r be T'k + 1, then the series whose general term T''k + 1 = Tk + 1 + T'k + 1 is also a G.P. with common ratio r.
the mathematical reasoning can be proved by observing the term of the sequences
Statement-I : 1, 2, 4, 8, ......... is a G.P., 4, 8, 16, 32 is a G.P. and 1 + 4, 2 + 8, 4 + 16, 8 + 32, ....... is also a G.P.
Statement-II : Let general term of a G.P. (with positive terms) with common ratio r be Tk + 1 and general term of another G.P. (with positive terms) with common ratio r be T'k + 1, then the series whose general term T''k + 1 = Tk + 1 + T'k + 1 is also a G.P. with common ratio r.
the mathematical reasoning can be proved by observing the term of the sequences
Let p, q, r R+ and 27 pqr ≥ (p + q + r)3 and 3p + 4q + 5r = 12 then p3 + q4 + r5 is equal to -
for real and positive numbers, we can use the property AM>=GM
Let p, q, r R+ and 27 pqr ≥ (p + q + r)3 and 3p + 4q + 5r = 12 then p3 + q4 + r5 is equal to -
for real and positive numbers, we can use the property AM>=GM
, the rate of formation of 
is 0.04 mole lit-1sec-1. Determine the rate of disappearance of 
and 
then which of the following indicates the relative ease with which the reaction moves?
