If the line y=x-1 bisects two chords of the parabola y^2=4bx which are passing through the point b,-2b, then the length of the latus rectum can be…

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If the line y=x-1 bisects two chords of the parabola y^2=4bx which are passing through the point b,-2b, then the length of the latus rectum can be equal to

MARKS Content Team · Accepted Answer

Correct answer: (A) 3. Any point on y=x–1 can be taken as h,h–1 Taking h,h-1 as the midpoint of chord, the equation of chord is yh-1-4b(x+h)/2=h-1^2-4bh Which passes through the point b,-2b ⇒ -2bh-1-2bb+h=h^2-2h+1-4bh ⇒ h^2-2h+2b^2-2b+1=0 As, above equation has two real roots, hence, -2^2-412b^2-2b+1>0 ⇒ 2b^2-2b<0⇒b<1⇒4b<4 ⇒ length of latus rectum is less than 4

If the line $y = x - 1$ bisects two chords of the parabola $y^{2} = 4 b x$ which are passing through the point $(b, - 2 b),$ then the length of the latus rectum can be equal to

Solution

More Parabola Questions

If the line y=x-1 bisects two chords of the parabola y2=4bx which are passing through the point b,-2b, then the length of the latus rectum can be equal to

Solution

More Parabola Questions

If the line $y = x - 1$ bisects two chords of the parabola $y^{2} = 4 b x$ which are passing through the point $(b, - 2 b),$ then the length of the latus rectum can be equal to