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Day 645: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 26 Jun 2022

    72
    Let CC be a circle passing through the points A(2,−1)A(2, - 1) and B(3,4)B(3,4). The line segment ABAB is not a diameter of CC. If rr is the radius of CC and its centre lies on the circle (x−5)2+(y−1)2=132(x - 5)^{2}+ (y - 1)^{2}=\frac{13}{2}, then r2r^{2} is equal to :

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  2. Question 2

    Conic Sections. Asked once: 25 Jun 2022

    160
    A circle touches both the y-axis and the line x+y=0x + y = 0. Then the locus of its center is

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  3. Question 3

    Conic Sections. Asked once: 25 Jun 2022

    79
    Let x=2t,y=t23x= 2t,y=\frac{t^{2}}{3} be a conic. Let SS be the focus and BB be the point on the axis of the conic such that SA⊥BASA\bot BA, where AA is any point on the conic. If kk is the ordinate of the centroid of ΔSAB\Delta SAB, then lim⁡t→1k\lim_{t \rightarrow 1} k is equal to

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  4. Question 4

    Conic Sections. Asked once: 25 Jun 2022

    61
    Let a circle CC touch the lines L1:4x−3y+K1L_{1}:4x- 3y+K_{1} =0= 0 and L2:4x−3y+K2=0, K1, K2∈RL_{2}:4x - 3y +K_{2}= 0,{\text{ }K}_{1},{\text{ }K}_{2}\in R. If a line passing through the centre of the circle CC intersects L1L_{1} at (−1,2)( - 1,2) and L2L_{2} at (3,−6)(3, - 6), then the equation of the circle CC is

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  5. Question 5

    Conic Sections. Asked once: 25 Jun 2022

    170
    The line y=x+1y = x + 1 meets the ellipse x24+y22=1\frac{x^{2}}{4}+\frac{y^{2}}{2}= 1 at two points PP and QQ. If rr is the radius of the circle with PQPQ as diameter then (3r)2(3r)^{2} is equal to

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