Home
Class 12
MATHS
The eccentricity of an ellipse whose cen...

The eccentricity of an ellipse whose centre is at the origin is `1/2`. If one of its directrices is x = - 4, then the equation of the normal to it at (1, 3/2) is :

A

`x+2y=4`

B

`2y-x=0`

C

`4x-2y=1`

D

`4x+2y=7`

Text Solution

Verified by Experts

The correct Answer is:
B
Given eccentricity `,e=1//2`
Also, from the given equation of the directrrix,
`-(a)/(e)=-4rArra=2`
Now, `b^(2) =a^(2)(1-e^(2))=4(1-(1)/(4))=3`
So, equation of ellipse is `(x^(2))/(4)+(y^(2))/(3)=1`
Differentiating w.r.t.x., we get
`(dy)/(dx)=-(3x)/(4y)`
`:. ((dy)/(dx))_((1,3//2)) =-(3)/(4)xx(2)/(3)=-(1)/(2)`
`:.` Slope of the rormal =2 is `y-(3)/(2)=2(x-1) or 4x-2y=1`
Promotional Banner

Similar Questions

Explore conceptually related problems

The eccentricity of an ellipes, with its centre at the origin, is 1/2. If one of the directrices is x=4, then the equation of the ellipse is-

The eccentricity of the ellipse 5x^(2) + 9y^(2) = 1 is _

The eccentricity of an ellipse is (1)/(2) and its one focus is at S(3,2) , if the vertex nearer of S be A (5,4) , find the equation of the ellipse .

The coordinates of the focus of an ellipse are (1,2) and eccentricity is (1)/(2) , the equation of its directrix is 3x + 4y - 5 = 0 . Find the equation of the ellipse.

find the equation of the ellipse whose eccentricities is 1/2, focus is (-1, 1), directrix is y = x + 3.

Find the equation of the ellipse whose eccentricity is (1)/(2) , focus is (2,0) anddirectix is x - 8 = 0

The eccentricity of the ellipse 4x^(2) + 25y^(2) = 100 is _

Find the equation of the ellipse whose centre lies at the origin,major axis lines on the x-axis,eccentricity is 2//3 and length of the latus rectum is 5 units.

The eccentricity of an ellipse is (1)/(sqrt(3)) , the coordinates of focus is (-2,1) and the point of intersection of the major axis and the directrix is (-2,3) . Find the coordinates of the centre of the ellipse and also equation of the ellipse .

The eccentricity of an ellipse is (4)/(5) and the coordinates of its one focus and the corresponding vertex are (8,2) and (9,2) . Find the equation of the ellipse. Also find in the same direction the coordinates of the point of intersection of its major axis and the directrix.