Question

The line 2x - y + 4 = 0 cuts the parabola y2 = 8x in P and Q. The midpoint of PQ is

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Answer 1

Let (h,k) be the mid-point of the chord 2x+y−4=

0 of the

parabola y

2

=4x. Then, its equation is ky−2(x+h)=k

2

−4h

Answer 2

Answer:

substituting y = 2x + 4 I. the equation of parabola .

* ( 2x+4 ) = 8x

* 4x2 + 16 x +16 = 8 x

* 4x2 + 8x +16 = 0

* x2 +2x +4 = 0

Let x1 ,x2 be the roots . then x1,x2 = -2

Now substituting x= y2/8 in the equation of the line we get

* 2( y2/8) - y +4 = 0

* y2/4 - y+4 = 0

* y2 -4y +16 =0

Let y1,y2 be the roots . then y1 + y2 = 4

Let us assume P be ( x1,y1 ) and Q be ( x2,y2 ) and R be the midpoint of PQ

* R = ( x1+x2 /2 , y1 +y2 / 2 )

* R = ( -2/2 , 4/2 )

Ans = R = ( -1,2 )