Q1 What are harmonic progressions and what is harmonic mean. Explain with formulas. Q2 If the ellipse passes through origin and has it foci ( 1,0) and (3,0) then find its equation.

Q3 If sinC + SinD = A and Cos C – Cos D = B then find the value of Tan (C – D)/2
Q4 The total number of ways of selecting Five Letters of the words INDEPENDENT. Also tell me the formula used.

Question

Nehal Wani · Answer

Ans 2.

Mid-pt of the foci gives the center of the ellipse.

Mid pt of (1,0) and (3,0) is (2,0)

Equation of major axis is the line joining the foci which is y=0

The ellipse passes through the origin. Therefore, Length of semi major axis is=a=2units

Distance between foci=2ae=2units

=> e=1/2

b²=a²(1-e²)=4(3/4)=3

Therefore Equation of ellipse:

[(x-2)²/4]+[(y)²/3]=1

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