Home
Class 12
MATHS
If the tangent at the point P(2,4) to th...

If the tangent at the point `P(2,4)` to the parabola `y^2=8x` meets the parabola `y^2=8x+5` at `Qa n dR ,` then find the midpoint of chord `Q Rdot`

Text Solution

Verified by Experts

The equation of the tangent to parabola `y^(2)=8x` at P(2,4) is
4y=4(x+2)
or x-y+2=0 (1)
This chord meets the parabola `y^(2)=8x+5` at Q and R.
Let `(x_(1),y_(1))` be the midpoint of chord QR.n
Then equation of QR is
`yy_(1)-4(x+x_(1))-5=y_(1)^(2)-8x_(1)-5" ""(Using "T=S_(1))`
`or" "4x-yy_(1)-4x_(1)+y_(1)^(2)=0` (2)
Clearly, (1) and (2) represent the same line.
`So," "(4)/(1)=-(y_(1))/(-1)=(-4x_(1)+y_(1)^(2))/(2)`
`rArr" "y_(1)=4and8=-4x_(1)+y_(1)^(2)`
`rArr" "y_(1)=4andx_(1)=2`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE ENGLISH|Exercise ILLUSTRATION 5.46|1 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise ILLUSTRATION 5.47|1 Videos

  • PARABOLA

    CENGAGE ENGLISH|Exercise ILLUSTRATION 5.44|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 the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Q and R , then find the midpoint of chord Q Rdot

The tangent at the point P(x_1, y_1) to the parabola y^2 = 4 a x meets the parabola y^2 = 4 a (x + b) at Q and R. the coordinates of the mid-point of QR are

A variable tangent to the parabola y^(2)=4ax meets the parabola y^(2)=-4ax P and Q. The locus of the mid-point of PQ, is

The equation of tangent at (8,8) to the parabola y^2=8x is ?

if the line 4x +3y +1=0 meets the parabola y^2=8x then the mid point of the chord is

A tangent to the parabola y^2 + 4bx = 0 meets the parabola y^2 = 4ax in P and Q. The locus of the middle points of PQ is:

If the chord of contact of tangents from a point P to the parabola y^2=4a x touches the parabola x^2=4b y , then find the locus of Pdot

If the chord of contact of tangents from a point P to the parabola y^2=4a x touches the parabola x^2=4b y , then find the locus of Pdot

Tangents drawn from the point A(-4, 8) to the parabola y^2 = 16x meet the parabola at P and Q . Then locus of the centre of the circle described on PQ as diameter is : (A) x^2 = -2a(y-a) (B) y^2 = -2a(x-a) (C) x^2 = 2a (y-a) (D) y^2 = 2a(x-a)

If the normal P(8,8) to the parabola y^(2) = 8x cuts It again at Q then find the length PQ