JEE Main 2022 · 27 Jul · Shift 1 · Mathematics Q29

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MathematicsInteger+4 / -1Question 29 of 90

If the length of the latus rectum of the ellipse $x^2+4y^2+2x+8y-\lambda=0$ is 4, and $l$ is the length of its major axis, then $\lambda+l$ is equal to ______.

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Answer and worked solution

Official answer: 75

Standard form. $(x+1)^2+4(y+1)^2=\lambda+5$ : $a^2=\lambda+5$ , $b^2=\frac{\lambda+5}4$ .

Latus rectum $\frac{2b^2}a=\frac{\sqrt{\lambda+5}}2=4$ , so $\lambda=59$ and $l=2a=16$ .

Answer: 75

Topics:Ellipse

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JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 29