Home
Class 12
MATHS
Length of the focal chord of the parabol...

Length of the focal chord of the parabola `y^2=4ax` at a distance p from the vertex is:

Text Solution

Verified by Experts

In the figure, OM = b = distance of focal chord PQ make an angle `theta` with positive x-axis.
`:." "PQ=4acosec^(2)theta`
Now, in right angled triangle OMS,
`sintheta=OM//OS=b//a`
`:." "PQ=4a(a//b)^(2)=4a^(3)//b^(2)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.33|1 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.34|1 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.31|1 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

If the length of a focal chord of the parabola y^2=4a x at a distance b from the vertex is c , then prove that b^2c=4a^3 .

Length of the shortest normal chord of the parabola y^2=4ax is

Knowledge Check

  • If (at^(2) , 2at) be the coordinate of an extremity of a focal chord of the parabola y^(2) =4ax, then the length of the chord is-

    A
    `a(t- (1)/(t)) ^(2)`
    B
    `a(t+ (1)/(t))`
    C
    `a(t +(1)/(t))^(2)`
    D
    `a(t- (1)/(t))`

    • Similar Questions

    Explore conceptually related problems

    Find the locus of the midpoint of the chords of the parabola y^2=4ax .which subtend a right angle at the vertex.

    Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

    Length of the focal chord of the parabola (y +3)^(2) = -8(x-1) which lies at a distance 2 units from the vertex of the parabola is

    If the point P(4, -2) is the one end of the focal chord PQ of the parabola y^(2)=x, then the slope of the tangent at Q, is

    Prove that the length of any chord of the parabola y^(2) = 4 ax passing through the vertex and making an angle theta with the positive direction of the x-axic is 4a cosec theta cot theta

    The length of the common chord of the parabolas y^(2)=x and x^(2)=y is

    Let PQ be a focal chord of the parabola y^(2)=4ax . The tangents to the parabola at P and Q meet at point lying on the line y=2x+a,alt0 . If chord PQ subtends an angle theta at the vertex of y^(2)=4ax , then tantheta=

    Home
    Profile