Home
Class 12
MATHS
If two chords drawn from the point A(4,4...

If two chords drawn from the point `A(4,4)` to the parabola `x^2=4y` are bisected by the line `y=m x ,` the interval in which `m` lies is `(-2sqrt(2),2sqrt(2))` `(-oo,-sqrt(2))uu(sqrt(2),oo)` `(-oo,-2sqrt(2)-2)uu(2sqrt(2)-2,oo)` none of these

Text Solution

Verified by Experts


Point (4,4) lies on the given parabola `x^(2)=4y`.
Any point on line y=mxis Q `(alpha,malpha)`.
Let the chord PR be bisected by Q.
`:." "alpha=(4+x_(1))/(2)rArrx_(2)=2alpha-4`
`andmalpha=(4+y_(1))/(2)rArry_(2)=2malpha-4`
Now, Q lies on the curve.
`:." "(2alpha-4)^(2)=4(2malpha-4)`
`rArr" "4alpha^(2)+16-16alpha=8(malpha-2)`
`rArr" "4alpha^(2)-8(2+m)alpha+32=0`
Since it is possible to draw two chords which get bisected at point Q, then above equation has two distinct real roots.
`:.` Discriminant, `Dgt0`
`rArr" "(8(2+m))^(2)-4xx4xx32gt0`
`rArr" "(2+m)^(2)-8gt0`
`rArr" "2+mgt2sqrt(2)or2+mgt-2sqrt(2)`
`rArr" "mgt2sqrt(2)-2ormlt-2sqrt(2)-2`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE ENGLISH|Exercise SOLVED EXAMPLES 5.13|1 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise SOLVED EXAMPLES 5.14|1 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise SOLVED EXAMPLES 5.11|1 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE ENGLISH|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE ENGLISH|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

If two chords drawn from the point A(4,4) to the parabola x^2=4y are bisected by the line y=m x , the interval in which m lies is (a) (-2sqrt(2),2sqrt(2)) (b) (-oo,-sqrt(2))uu(sqrt(2),oo) (c) (-oo,-2sqrt(2)-2)uu(2sqrt(2)-2,oo) (d) none of these

The set of all real numbers x for which x^2-|x+2|+x >0 is (-oo,-2) b. (-oo,-sqrt(2))uu(sqrt(2),oo) c. (-oo,-1)uu(1,oo) d. (sqrt(2),oo)

lim_(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)

lim_(n to oo)[(sqrt(n+1)+sqrt(n+2)+....+sqrt(2n))/(n sqrt((n)))]

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

(sqrt(3)-1)+(1)/(2)(sqrt(3)-1)^(2)+(1)/(3)(sqrt(3)-1)^(3)+….oo

If the ellipse (x^2)/(a^2-7)+(y^2)/(13=5a)=1 is inscribed in a square of side length sqrt(2)a , then a is equal to 6/5 (-oo,-sqrt(7))uu(sqrt(7),(13)/5) (-oo,-sqrt(7))uu((13)/5,sqrt(7),) no such a exists

evaluate sqrt(-2+2sqrt(-2+2sqrt(-2+..............oo))

The domain of the function f(x)=sqrt(10-sqrt(x^4-21 x^2)) is a) [5,oo) b. [-sqrt(21),sqrt(21)] c. [-5,-sqrt(21)]uu[sqrt(21),5]uu{0] d. (-oo,-5)

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a