Mathematics · 2025
JEE Main · 29 January 2025, Shift 2 · Q12
If α x+β y=109 is the equation of the chord of the ellipse x^2/9+y^2/4=1, whose mid point is (5/2, 1/2), then α+β is equal to:
If $\displaystyle \alpha x+\beta y=109$ is the equation of the chord of the ellipse $\displaystyle \frac{x^2}{9}+\frac{y^2}{4}=1$, whose mid point is $\displaystyle \left(\frac{5}{2}, \frac{1}{2}\right)$, then $\displaystyle \alpha+\beta$ is equal to :
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle 58$
More from Ellipse
- Let the line y-x=1 intersect the ellipse x^2/2+y^2/1=1 at the points A and B. Then the angle made by the line segment AB at the center of the ellipse…2026
- Let (h, k) lie on the circle C: x^2+y^2=4 and the point (2 h+1,3 k+2) lie on an ellipse with eccentricity e. Then the value of 5/e^2 is equal to ____.2026
- The equation of the chord, of the ellipse x^2/25+y^2/16=1, whose mid-point is (3,1) is:2025
- The length of the latus-rectum of the ellipse, whose foci are (2,5) and (2,-3) and eccentricity is 4/5, is2025
- The length of the chord of the ellipse x^2/4+y^2/2=1, whose mid-point is (1, 1/2), is:2025
- Let x=9 be a directrix of an ellipse E, whose centre is at the origin and eccentricity is 1/3. Let P(α, 0), α>0, be a focus of E and AB be a chord…2026
- If the midpoint of a chord of the ellipse x^2/9+y^2/4=1 is (√2, 4 / 3), and the length of the chord is (2 √α)/3, then α is:2025
- Consider the parabola P: y^2=4 k x and the ellipse E: x^2/a^2+y^2/b^2=1. Let the line segment joining the points of intersection of P and E, be their…2026
JEE Main 2025 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.