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Day 647: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 2021 Paper 26

    64
    Let A(1,4)A(1,4) and B(1,−5)B(1, - 5) be two points. Let PP be a point on the circle (x−1)2+(y−1)2=1(x - 1)^{2}+ (y - 1)^{2}= 1 such that (PA)2+(PB)2(PA)^{2}+ (PB)^{2} have maximum value, then the points, P,AP,A and BB lie on:

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  2. Question 2

    Conic Sections. Asked once: 2021 Paper 25

    80
    In the circle given below, let OA=1OA = 1 unit, OB=13OB = 13 unit and PQ⊥OBPQ\bot OB. Then, the area of the triangle PQBPQB (in square units) is:

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  3. Question 3

    Conic Sections. Asked once: 2021 Paper 23

    85
    A tangent line LL is drawn at the point (2,−4)(2, - 4) on the parabola y2=8xy^{2}= 8x. If the line LL is also tangent to the circle x2+y2=ax^{2}+y^{2}=a, then 'a' is equal to

  4. Question 4

    Conic Sections. Asked once: 2021 Paper 22

    74
    The length of the latus rectum of a parabola, whose vertex and focus are on the positive xx-axis at a distance RR and S(>R)S( > R) respectively from the origin, is:

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  5. Question 5

    Conic Sections. Asked once: 2021 Paper 22

    86
    If the variable line 3x+4y=α3x + 4y = \alpha lies between the two circles (x−1)2+(y−1)2=1(x - 1)^{2}+ (y - 1)^{2}= 1 and (x−9)2+(y−1)2=4(x - 9)^{2}+ (y - 1)^{2}= 4, without intercepting a chord on either circle, then the sum of all the integral values of α\alpha is