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The length of major ofthe ellipse (5x-10...

The length of major ofthe ellipse `(5x-10)^2 +(5y+15)^2 = 1/4(3x-4y+7)^2` is

A

10

B

`20//3`

C

`20//7`

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
`(5x-10)^(2)+(5y+15)^(2)=((3x-4y+7)^(2))/(4)`
`or (x-2)^(2)+(y+3)^(2)=((1)/(2)(3x-4y+7)/(5))^(2)`
`or sqrt((x-2)^(2)+(y-3)^(2))=(1)/(2)(|3x-4y+7|)/(5)`
It is an ellipse , whose focus is (2,-3) directrix is 3x-4y+7=0, and eccentricity is 1/2.
Length of perpendicular from the focus to the drectrix is `(|3xx2-4(-3)+7|)/(5)=5`
or `(a)/(e)-ae=5`
`or 2a-(a)/(2)=5`
`or a=(10)/(3)`
So, the length of the major of axis is 20/3
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