Conic Sections

JEE Main · Mathematics · 17 past questions

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14 of 17 · show all

1. Q1 2026 2 Apr Shift 1

   Let an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, $a<b$, pass through the point $(4,3)$ and have…

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2. Q2 2026 2 Apr Shift 2

   Let O be the origin, and P and Q be two points on the rectangular hyperbola $xy=12$ such that the mid point…

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3. Q3 2026 2 Apr Shift 2

   Let the parabola $y = x^2 + px + q$ passing through the point $(1, -1)$ be such that the distance between its…

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4. Q5 2026 4 Apr Shift 1

   Consider the parabola $P: y^2 = 4kx$ and the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. Let the line…

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5. Q6 2026 4 Apr Shift 2

   Let $H: \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ be a hyperbola such that the distance between its foci is 6…

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6. Q8 2026 5 Apr Shift 1

   Let a focus of the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ be $S(4, 0)$ and its eccentricity be…

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7. Q9 2026 5 Apr Shift 2

   Let the directrix of the parabola P : $y^2 = 8x$, cut x-axis at the point A. Let B $(\alpha, \beta)$…

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8. Q10 2026 5 Apr Shift 2

   Let the eccentricity e of a hyperbola satisfy the equation $6e^2 - 11e + 3 = 0$. If the foci of the hyperbola…

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9. Q11 2026 6 Apr Shift 1

   Let one root of the quadratic equation in $x$: $(k^2-15k+27)x^2+9(k-1)x+18=0$ be twice the other. Then the…

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10. Q12 2026 6 Apr Shift 1

    Let $e_1$ and $e_2$ be two distinct roots of the equation $x^2-ax+2=0$. Let the sets $\{a\in\mathbb{R}: e_1$…

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11. Q13 2026 6 Apr Shift 1

    If the eccentricity $e$ of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, passing through $(6,4\sqrt3)$…

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12. Q15 2026 6 Apr Shift 2

    The eccentricity of an ellipse E with centre at the origin O is $\frac{\sqrt{3}}{2}$ and its directrices are…

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13. Q16 2026 6 Apr Shift 2

    Let $x = 9$ be a directrix of an ellipse E, whose centre is at the origin and eccentricity is $\frac{1}{3}$.…

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14. Q17 2026 8 Apr Shift 2

    Let O be the vertex of the parabola y^2=4x and its chords OP and OQ are perpendicular to each other. If the…

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