Question
The eccentricity of the ellipse represented by the equation 25x2 + 16y2 – 150x – 175 = 0 is -
- None of these
Hint:
convert the given equation into the standard form of ellipse and find out the values of a,b. then use the formula for calculating the eccentricity
The correct answer is:
3/5
converting the equation into the whole square form for x and y , we get
25x2-150x+16y2-175=0
25(x2-6x)+ 16y2-175=0
25(x2-6x+9)+16y2-175- 225=0
25(x-3)2+16(y2)=400
(x-3)2 /16+ y2 /25=1
b=5 and a=4
b>a so, it is a vertical ellipse.
e=√(1-a2/b2)= √9/25 = 3/5
the given equation has to be converted into the whole square form for x and y so that the standard form of ellipse can be observed. from the standard form, the eccentricity can be calculated by the values of a and b.
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