Home
Class 12
MATHS
If a chord, which is not a tangent of th...

If a chord, which is not a tangent of the parabola `y^2=16 x` has the equation `2x+y=p ,` and midpoint `(h , k),` then which of the following is(are) possible values (s) of `p , h and k ?`
`p=-1,h=1,k=-3`
`p=2, h=3, k=-4`
`p=-2, h=2, k=-4`
`p=5, h=4, k=-3`

Text Solution

Verified by Experts

The correct Answer is:
B
Parabola,`y^2-16x=0` equation of chord.`2x+y=p`
The equation of chord at given middle point(h,k) to the parabola
`T=s_1`
`ky-8(x+h)=k^2-16h`
`ky-8x+8h-k^2=0`
`2x+y-p=0`
`-8/2=k/1=(8h-k^2)/(-p)`
`2k=-8`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If a chord, which is not a tangent, of the parabola y^(2)=16x has the equation 2x+y=p, and midpoint (h,k), then which of the following is (are) possible value(s) of p,h and k ?

If a chord which is not a tangent, of the parabola y^(2)=16x has the equation 2x+y=p, and mid-point (h, k), then which of the following is (are) possible value (s) of p, h and k?

If two parabolas y^(2)=4a(x-k) and x^(2)=4a(y-k) have only one common point P, then the coordinates of P are

If the line y=x+c touches the hyperbola (x^(2))/(9)-(y^(2))/(5)=1 at the point P(h, k), then (h, k) can be equal to

The roots of the equation m^2-4m+5=0 are the slopes of the two tangents to the parabola y^2=4x . The tangents intersect at the point (h, k). Then h + k is equal to:

Let a point P(h,k) satisfies the equation x^(3)+y^(3)+3xy=1 .Then the locus of the point P is

The fouce of the rectangular hyperbola (x-h) (y-k) =p^(2) is

If two parabolas y^(2)-4a(x-k) and x^(2)=4a(y-k) have only one common point P, then the equation of normal to y^(2)=4a(x-k) at P is

For the reaction C_(2)H_(4)(g) + H_(2)(g) rarr C_(2)H_(6)(g) , which of the following expressions between K_(p) "and" K_(c) is true at 27^(@)C ?