If the ellipse (x²)/(a²)+(y²)/(b²)=1 meets the line x/7+y/(2 √(6))=1 on the x -axis and the line x/7-y/(2 √(6))=1 on the y -axis, then the eccentricity of the ellipse is:

Coordinate Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jul, Evening shift · Q3763

JEE Main 202225 Jul, Evening shiftMathematicsMediumCoordinate Geometry478× since 2002

If the ellipse

\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1

meets the line

\frac{x}{7}+\frac{y}{2 \sqrt{6}}=1

on the

x

-axis and the line

\frac{x}{7}-\frac{y}{2 \sqrt{6}}=1

on the

y

-axis, then the eccentricity of the ellipse is :

JEE Main 2022 · 25 Jul, Evening shift · Q3763

JEE Main 202225 Jul, Evening shiftMathematicsMediumCoordinate Geometry478× since 2002

If the ellipse

\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1

meets the line

\frac{x}{7}+\frac{y}{2 \sqrt{6}}=1

on the

x

-axis and the line

\frac{x}{7}-\frac{y}{2 \sqrt{6}}=1

on the

y

-axis, then the eccentricity of the ellipse is :