Home
Class 12
MATHS
A parabola is drawn through two given po...

A parabola is drawn through two given points `A(1,0)` and `B(-1,0)` such that its directrix always touches the circle `x² + y^2 = 4.` Then, The locus of focus of the parabola is=

A

`(x^(2))/(4) +(y^(2))/(3) = 1`

B

`(x^(2))/(4) +(y^(2))/(5) =1`

C

`(x^(2))/(3)+(y^(2))/(4) = 1`

D

`(x^(2))/(5)+(y^(2))/(4)=1`

Text Solution

Verified by Experts

The correct Answer is:
A
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Matching Column Type|1 Videos

  • PARABOLA

    CENGAGE|Exercise Question Bank|21 Videos

  • PARABOLA

    CENGAGE|Exercise Multiple Correct Answers Type|10 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Question Bank|19 Videos

Similar Questions

Explore conceptually related problems

A parabola is drawn through two given points A(1,0,0) and B(-1,0) such that its directrix always touches the circle x^(2)+y^(2)=4. Then The locus of focus of the parabola is=

A movable parabola touches x-axis and y-axis at (0,1) and (1,0). Then the locus of the focus of the parabola is:

Knowledge Check

  • A parabola is drawn through two given points A (2, 0) and B(-2, 0) such that its directrix always touch the circle x^2 + y^2 = 16 , then locus of focus of the parabola is

    A
    `3x^2 + 4y^2 = 48 `
    B
    `4x^2 + 3y^2 = 48 `
    C
    `3x^2 + 4y^2 = 60 `
    D
    `4x^2 + 3y^2 = 60 `

  • A parabola having directrix x +y +2 =0 touches a line 2x +y -5 = 0 at (2,1). Then the semi-latus rectum of the parabola, is

    A
    8
    B
    `(9)/(sqrt(2))`
    C
    `(10)/(sqrt(2))`
    D
    `(11)/(sqrt(2))`

  • Consider a circle with its centre lying on the focus of the parabola y^(2) = 2px such that it touches the directrix of the parabola. Then, the point of intersection of the circle and the parabola is

    A
    `((p)/(2),p)` or `((p)/(2),-p)`
    B
    `((p)/(2),(-p)/(2))`
    C
    `((-p)/(2),p)`
    D
    `((-p)/(2),(-p)/(2))`

    • Similar Questions

    Explore conceptually related problems

    Consider two concentric circles C_(1):x^(2)+y^(2)=1 and C_(2):x^(2)+y^(2)-4=0 .A parabola is drawn through the points where c_(1) ,meets the x -axis and having arbitrary tangent of C_(2) as directrix.Then the locus of the focus of drawn parabola is (A) "(3)/(4)x^(2)-y^(2)=3, (B) (3)/(4)x^(2)+y^(2)=3, (C) An ellipse (D) An hyperbola

    If the focus =(2,3)and directrix is x+y=1 then the equation of the parabola is ____.

    The directrix of a parabola is 2x-y=1. The focus lies on y-axis.The locus of one end of the latus rectum is

    A variable circle is described to pass through the point (1,0) and tangent to the curve y=tan(tan^(-1)x). The locus of the centre of the circle is a parabola whose

    A variable circle is described to passes through the point (1, 0) and tangent to the curve y = tan(tan^(-1)x) . The locus of the centre of the circle is a parabola whose

    Home
    Profile