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Day 649: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 2021 Paper 16

    49
    From the point (−1,1)( - 1,1) two tangents are drawn to x2+y2−2x−6y+6=0x^{2}+y^{2}- 2x- 6y+ 6 = 0 that touch the circle at AA and BB. A point DD on the circle such that AD=ABAD=AB. Find the area of △ABD\bigtriangleup ABD.

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  2. Question 2

    Conic Sections. Asked once: 2021 Paper 14

    47
    For a parabola, it's vertex is at a distance of 2 units from origin, focus is at distances of 4 units from origin. A pair of tangents are drawn from origin to the parabola which meet it at PP and QQ. Find area of △OPQ(O:\bigtriangleup OPQ(O: origin).

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  3. Question 3

    Conic Sections. Asked once: 2021 Paper 12

    55
    Let PP be a variable point on the parabola y=4x2+1y= 4x^{2}+ 1. Then, the locus of the mid-point of the point PP and the foot of the perpendicular drawn from the point PP to the line y=xy = x is:

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  4. Question 4

    Conic Sections. Asked once: 2021 Paper 12

    41
    Let r1r_{1} and r2r_{2} be the radii of the largest and smallest circles, respectively, which pass through the point (−4,1)( - 4,1) and having their centres on the circumference of the circle x2+y2+2x+4y−4=0x^{2}+y^{2}+ 2x+ 4y- 4 = 0. If r1r2=a+b2\frac{r_{1}}{r_{2}}=a+b\sqrt{2}, then a+ba+b is equal to:

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  5. Question 5

    Conic Sections. Asked once: 2021 Paper 10

    72
    Let S1:x2+y2=9S_{1}:x^{2}+y^{2}= 9 and S2:(x−2)2+y2=1S_{2}:(x- 2)^{2}+y^{2}= 1. Then the locus of center of a variable circle SS which touches S1S_{1} internally and S2S_{2} externally always passes through the points :

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