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Day 644: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 27 Jun 2022

    88
    A rectangle RR with end points of the one of its sides as (1,2)(1,2) and (3,6)(3,6) is inscribed in a circle. If the equation of a diameter of the circle is 2x−y+4=2x-y+ 4 = 0 , then the area of RR is

  2. Question 2

    Conic Sections. Asked once: 27 Jun 2022

    89
    A circle of radius 2 unit passes through the vertex and the focus of the parabola y2=2xy^{2}= 2x and touches the parabola y=(x−14)2+αy=\left( x-\frac{1}{4} \right)^{2}+\alpha, where α>0\alpha> 0. Then (4α−8)2(4\alpha- 8)^{2} is equal to

  3. Question 3

    Conic Sections. Asked once: 27 Jun 2022

    64
    Let dydx=ax−by+abx+cy+a\frac{dy}{dx}=\frac{ax - by + a}{bx + cy + a}, where a,b,ca,b,c are constants, represent a circle passing through the point (2,5)(2,5). Then the shortest distance of the point (11,6)(11,6) from this circle is:

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  4. Question 4

    Conic Sections. Asked once: 26 Jun 2022

    73
    Let the normal at the point PP on the parabola y2=y^{2}= 6x6x pass through the point (5,−8)(5, - 8). If the tangent at PP to the parabola intersects its directrix at the point QQ, then the ordinate of the point QQ is:

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  5. Question 5

    Conic Sections. Asked once: 26 Jun 2022

    178
    Let a line L1L_{1} be tangent to the hyperbola x216−y24=1\frac{x^{2}}{16}-\frac{y^{2}}{4}= 1 and let L2L_{2} be the line passing through the origin and perpendicular to L1L_{1}. If the locus of the point of intersection of L1L_{1} and L2L_{2} is (x2+y2)2=\left( x^{2}+y^{2} \right)^{2}= αx2+βy2\alpha x^{2}+ \beta y^{2}, then α+β\alpha + \beta is equal to