Home
Class 12
MATHS
Find the points on the ellipse (x^2)/4+(...

Find the points on the ellipse `(x^2)/4+(y^2)/9=1` on which the normals are parallel to the line `2x-y=1.`

Text Solution

Verified by Experts

The normal at `P(2 cos theta,3 sin theta)` is `(2x)/(cos theta)-(3y)/(sin theta)=-5`
Now, this normal is parallel to 2x-y1. Then, `(2//cos theta)/(3//sin theta)=2`
or ` tan theta=(3)/(1)`
`cos theta=+-and sin theta=+-(3)/(sqrt(10))`
Hence, the points are `(2sqrt(10),9sqrt10),(-2//sqrt(10),-9//sqrt(10))`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the co-ordinates for the points on the ellipse x^2+3y^2=37 at which the normal is parallel to the line 6x-5y=2.

Find the points on the curve (x^2)/9+(y^2)/(16)=1 at which the tangents are parallel to the x-axis and y-axis.

Find the points on the curve y=x^3-2x^2-x at which the tangent lines are parallel to the line y=3x-2

Find the points on the curve y=x^3-2x^2-x at which the tangent lines are parallel to the line y=3x-2 .

Find points on the curve (x^2)/9-(y^2)/(16)=1 at which the tangents are parallel to the x-axis and y-axis.

Find the number of rational points on the ellipse (x^2)/9+(y^2)/4=1.

Find the number of rational points on the ellipse (x^2)/9+(y^2)/4=1.

Find the points on the curve 4x^2+9y^2=1 , where the tangents are perpendicular to the line 2y+x=0 .

Find the points on the curve 4x^2+9y^2=1 , where the tangents are perpendicular to the line 2y+x=0

A point on the ellipse x^2+3y^2=37 where the normal is parallel to the line 6x-5y=2 is (5,-2) (b) (5, 2) (c) (-5,2) (d) (-5,-2)