Let the hyperbola H: (x²)/(a²)-(y²)/(b²)=1 pass through the point (2 √(2),-2 √(2)). A parabola is drawn whose focus is same as the focus of H with positive abscissa and the directrix of the parabola passes through the other focus of H. If the length of the latus rectum of the parabola is e times the length of the latus rectum of H, where e is the eccentricity of H, then which of the following points lies on the parabola?

Coordinate Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 28 Jul, Evening shift · Q3976

JEE Main 202228 Jul, Evening shiftMathematicsMediumCoordinate Geometry478× since 2002

Let the hyperbola

H: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1

pass through the point

(2 \sqrt{2},-2 \sqrt{2})

. A parabola is drawn whose focus is same as the focus of

\mathrm{H}

with positive abscissa and the directrix of the parabola passes through the other focus of

\mathrm{H}

. If the length of the latus rectum of the parabola is e times the length of the latus rectum of

\mathrm{H}

, where e is the eccentricity of H, then which of the following points lies on the parabola?

JEE Main 2022 Coordinate Geometry Question with Solution (28 Jul Evening shift, Q3976) | JEE Arc