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Day 646: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Conic Sections. Asked once: 25 Jun 2022

    168
    If the line y=4+kx,k>0y = 4 + kx,k > 0, is the tangent to the parabola y=x−x2y = x -x^{2} at the point PP and VV is the vertex of the parabola, then the slope of the line through PP and VV is:

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  2. Question 2

    Conic Sections. Asked once: 14 Jun 2022

    88
    If two tangents drawn from a point (α,β)(\alpha,\beta) lying on the ellipse 25x2+4y2=125x^{2}+ 4y^{2}= 1 to the parabola y2=4xy^{2}= 4x are such that the slope of one tangent is four times the other, then the value of (10α+5)2+(16β2+50)2(10\alpha+ 5)^{2}+\left( 16\beta^{2}+ 50 \right)^{2} equals

  3. Question 3

    Conic Sections. Asked once: 14 Jun 2022

    159
    Let the maximum area of the triangle that can be inscribed in the ellipse x2a2+y24=1,a>2\frac{x^{2}}{a^{2}}+\frac{y^{2}}{4}= 1,a > 2, having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the y-axis, be 636\sqrt{3}. Then the eccentricity of the ellispe is:

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  4. Question 4

    Conic Sections. Asked once: 14 Jun 2022

    177
    Let a circle C:(x−h)2+(y−k)2=r2,k>0C:(x - h)^{2}+ (y - k)^{2}=r^{2},k > 0, touch the xx-axis at (1,0)(1,0). If the line x+y=0x + y = 0 intersects the circle CC at PP and QQ such that the length of the chord PQPQ is 2 , then the value of h+k+rh + k + r is equal to

  5. Question 5

    Conic Sections. Asked once: 14 Jun 2022

    179
    Let the hyperbola H:x2a2−y2=1H:\frac{x^{2}}{a^{2}}-y^{2}= 1 and the ellipse E : 3x2+4y2=123x^{2}+ 4y^{2}= 12 be such that the length of latus rectum of HH is equal to the length of latus rectum of EE. If eHe_{H} and eEe_{E} are the eccentricities of HH and EE respectively, then the value of 12(eH2+eE2)12\left( e_{H}^{2}+e_{E}^{2} \right) is equal to