PYQ Vault
EbooksTutor

Shortest distance from a point or circle to a parabola

This type of question, asked 4 times: 30 Jan 2023, 27 Jan 2024, 23 Jan 2025, 3 Apr 2025. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    30 Jan 2023

    66
    If P(h,k)P(h,k) be a point on the parabola x=4y2x = 4y^{2}, which is nearest to the point Q(0,33)Q(0,33), then the distance of PP from the directrix of the parabola y2=4(x+y)y^{2}= 4(x + y) is equal to:

    Tap an option to check your answer.

  2. Question 2

    27 Jan 2024

    67
    If the shortest distance of the parabola y2=4xy^{2}= 4x from the centre of the circle x2+y2−4x−16y+64=0x^{2}+y^{2}- 4x - 16y + 64 = 0 is dd, then d2d^{2} is equal to :

    Tap an option to check your answer.

  3. Question 3

    23 Jan 2025

    138
    Let the shortest distance from (a,0),a>0(a,0),a > 0, to the parabola y2=4xy^{2}= 4x be 4 . Then the equation of the circle passing through the point (a,0)(a,0) and the focus of the parabola, and having its centre on the axis of the parabola is:

    Tap an option to check your answer.

  4. Question 4

    3 Apr 2025

    143
    The shortest distance between the curves y2=8xy^{2}= 8x and x2+y2+12y+35=0x^{2}+y^{2}+ 12y+ 35 = 0 is :

    Tap an option to check your answer.