What is the equation of an ellipse when it's centre is at (0,0) and it's axes are parallel to the coordinate axes. It's eccentricity is 1/sqrt2 and the length of major axis is 5
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First of all the eq of an ellipse is (x^2/a^2)+(y^2/b^2)=1
Now to find a and b,
(a=length of semi major axis, b=length of semi minor axis)
therefore a=5/2 (given) b=?
therefore eccentricity of an ellipse=> e^2=1-(b^2/a^2)
thus, 1/2 = 1-b^2/(5/2)^2
=> 1/2 = 1-b^2/25/4 => 1/2=4b^2/25 => b^2 = 1/2*25/4 => b^2 = 25/8
=> thus b = sqrt(25/8)
now as we have got the values of a and b, the equation of an ellipse with a=5/2 and b=sqrt(25/8) thus substituting the values of a and b we get,
{x^2/25/4}+{y^2/25/8}=1 which is the required equation.
Now to find a and b,
(a=length of semi major axis, b=length of semi minor axis)
therefore a=5/2 (given) b=?
therefore eccentricity of an ellipse=> e^2=1-(b^2/a^2)
thus, 1/2 = 1-b^2/(5/2)^2
=> 1/2 = 1-b^2/25/4 => 1/2=4b^2/25 => b^2 = 1/2*25/4 => b^2 = 25/8
=> thus b = sqrt(25/8)
now as we have got the values of a and b, the equation of an ellipse with a=5/2 and b=sqrt(25/8) thus substituting the values of a and b we get,
{x^2/25/4}+{y^2/25/8}=1 which is the required equation.
Swayam2504:
Sorry, I typed the wrong question. The length of the MINOR axis is 5
arerreee but you got the method na so now you solve it
can*
I got the method. But while solving the equation to find the value of a, the variables are getting cancelled. You check it.
wait lemme check
nothing is getting cancelled brother the value of a is coming to be 5/sqrt(2) now substitute this value in the equation
you just try it once again you must have committed a silly mistake
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