Question
If line – 
+ 
= 
touches ellipse 
+ 
= 1 then its eccentric angle 
is
- 0
- 45º
- 60º
- 135º
Hint:
compare the general equation of tangent of an ellipse with thee given equation.
The correct answer is: 135º
135º
Equation of tangent of an ellipse of the given form is :
x cos Ѳ/a + ysin Ѳ/b=1
given tangent : – + =
on comparing the two equations, we get
cos Ѳ/-1 = sin Ѳ /1 = 1/√2
Ѳ = 135 degree
the general coordinates of an ellipse are substituted into the equation of ellipse to find the general equation of tangent of an ellipse. the angle lies in the 2nd quadrant so the cosine is negative but the sine is positive of the angle.
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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 
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the AM GM rule is valid for any set of natural numbers, i.e., numbers > 0.
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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
