Skip to main content
Back to Conic Sections
JEE Main 2021
Conic Sections
Ellipse
Easy

Question

If the tangent at a point on the ellipse x227+y23=1{{{x^2}} \over {27}} + {{{y^2}} \over 3} = 1 meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle OAB is :

Options

Solution

Key Concept: Tangent to an Ellipse and Area of a Triangle Formed by Intercepts

The problem asks for the minimum area of the triangle formed by the origin (O), and the x and y-intercepts (A and B) of a tangent to a given ellipse. A crucial concept here is the equation of the tangent to an ellipse in parametric form, which simplifies the calculation of intercepts.

For an ellipse with the standard equation x2a2+y2b2=1\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

  1. The parametric coordinates of a point on the ellipse are (acos⁡θ,bsin⁡θ)(a\cos\theta, b\sin\theta).
  2. The equation of the tangent to the ellipse at the point
Previous QuestionNext Question

Practice More Conic Sections Questions

View All Questions