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Day 648: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 2021 Paper 21

    66
    If two tangents drawn from a point PP to the parabola y2=16(x−3)y^{2}= 16(x- 3) are at right angles, then the locus of point PP is :

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  2. Question 2

    Conic Sections. Asked once: 2021 Paper 21

    86
    Let A(sec⁡θ, 2tan⁡θ)A(\sec\theta,\ 2\tan\theta) and B(sec⁡ϕ, 2tan⁡ϕ)B(\sec\phi,\ 2\tan\phi), where θ+ϕ=π2\theta+\phi=\dfrac{\pi}{2}, be two points on the hyperbola 2x2−y2=22x^{2}-y^{2}=2. If (α,β)(\alpha,\beta) is the point of intersection of the normals to the hyperbola at AA and BB, then (2β)2(2\beta)^{2} is equal to ____.

  3. Question 3

    Conic Sections. Asked once: 2021 Paper 20

    74
    A tangent and a normal are drawn at the point P(2,−4)P(2, - 4) on the parabola y2=8xy^{2}= 8x, which meet the directrix of the parabola at the points AA and BB respectively. If Q(a,b)Q(a,b) is a point such that AQBPAQBP is a square, then 2a+b2a+b is equal to:

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  4. Question 4

    Conic Sections. Asked once: 2021 Paper 20

    83
    Let the equation x2+y2+px+(1−p)y+5=0x^{2}+y^{2}+px+ (1 -p)y+ 5 = 0 represent circles of varying radius r∈(0,5]r\in (0,5\rbrack. Then the number of elements in the set S={q:q=p2 and q is an integer}S=\{q : q=p^{2} \text{ and } q \text{ is an integer}\} is:

  5. Question 5

    Conic Sections. Asked once: 2021 Paper 18

    73
    If a line along a chord of the circle 4x2+4y2+120x+675=04x^{2}+ 4y^{2}+ 120x + 675 = 0, passes through the point (−30,0)( - 30,0) and is tangent to the parabola y2=30xy^{2}= 30x, then the length of this chord is:

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