Home
Class 12
MATHS
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

Verified by Experts

Let the centre of the ellipse be C(x,y)
Clearly, axeas are tangents to the ellipse to the ellipse which are perpendicular and intesect at origin O.
So, origin lies on the director circle
Thus, origin lies on the director circle.
OC is radius of he director circle .
So, `OC^(2)=a^(2)+b^(2)=22+12`
or `x^(2)+y^(2)=5`
Promotional Banner

Similar Questions

Explore conceptually related problems

A circle is drawn to cut a chord of length 2a unit along x-axis and to touch the y-axis. Then the locus of the centre of the circle is-

The eccentric angle in the first quadrant of a point on the ellipse (x^(2))/(10) +(y^(2))/(8) = 1 at a distance 3 units from the centre of the ellipse is _

If the angle between the lines joining the end points of minor axis of an elipes with its one focus is pi/2, then the eccentricity of the ellipse is-

If the major and minor axes of the ellipse are the axes of coordinates, then the equation of the ellipse passing through the points (2,-2) and (-3,1) is-

Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse 9x^(2)+4y^(2)=36

If the length of the minor axis of an ellipse is equal to the distance between their foci, then eccntricity of the ellipse is _

An ellipse is drawn with major and minor axis of length 10 and 8 respectively. Using one focus a centre, a circle is drawn that is tangent to ellipse, with no part of the circle being outside the ellipse. The radius of the circle is

A rod of length a unit slides on the x-axis and another rod of length b unit slides on the y-axis in such a way that the four extremities of the rod are concylic. Show that the locus of the centre of the circle is 4(x^(2)-y^(2))=a^(2)-b^(2) .

Find the eccentricity of the ellipse if the length of minor axis is equal to half the distance between the foci of the ellipse .

Let the length of latus rectum of an ellipse with its major axis along x-axis and center at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of the minor axis , then which of the following points lies on it: (a) (4sqrt2, 2sqrt2) (b) (4sqrt3, 2sqrt2) (c) (4sqrt3, 2sqrt3) (d) (4sqrt2, 2sqrt3)