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An ellipse hase semi-major of length 2 a...

An ellipse hase semi-major of length 2 and semi-minor axis of length 1. It slides between the coordinates axes in the first quadrant while mantaining contact with both x-axis and y-axis. The locus of the centre of the ellipse is

A

`x^(2)+y^(2)=8`

B

`(x^(2))/(9)+(y^(2))/(4)=1`

C

`y^(2)=4x`

D

`x^(2)+y^(2)=5`

Text Solution

AI Generated Solution

To find the locus of the center of the ellipse that slides between the coordinate axes in the first quadrant while maintaining contact with both the x-axis and y-axis, we can follow these steps: ### Step 1: Understand the dimensions of the ellipse The semi-major axis (a) is given as 2, and the semi-minor axis (b) is given as 1. ### Step 2: Identify the center of the ellipse Let the center of the ellipse be at the point (h, k). Since the ellipse maintains contact with the x-axis and y-axis, the distances from the center to the axes must be equal to the semi-major and semi-minor axes. ...
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