The set of values of - - - for which three distinct chords drawn from - 0 to the ellipse x2-2 y2-1 are bisected by the parabola y2-4 x is

Find the condition on a and b for which two distinct chords of the ellipse $\frac{x^{2}}{2 a^{2}} + \frac{y^{2}}{2 b^{2}} = 1$ passing
through $(a, - b)$ are bisected by the line $x + y = b .$

Q. Tangents are drawn to the ellipse

\frac{x^{2}}{36} + \frac{y^{2}}{9} = 1

from any point on the parabola

y^{2} = 4 x .

The corresponding chord of contact will touch a parabola, whose equation is

Q. Set of values of

α

for which the point

(α, 1)

lies inside the curves

C_{1} : x^{2} + y^{2} - 4 = 0

and

C_{2} : y^{2} = 4 x

Join BYJU'S Learning Program

The set of values of 'α' for which three distinct chords drawn from (α, 0) to the ellipse x2+2y2=1 are bisected by the parabola y2 = 4x is

The correct option is D (8,4+√17)Let the middle pt of chord be (t2, 2t). Mid pt of chord must lie inside the ellipse ⇒t4+8t2−1<0 t2ϵ(0,−4+√17) eqn. of chord is t2x+4ty=t4+8t2 ∴∝ϵ(8,4+√17)

The set of values of ' $α$ ' for which three distinct chords drawn from ( $α$ , 0) to the ellipse $x^{2} + 2 y^{2} = 1$ are bisected by the parabola $y^{2}$ = 4x is

The correct option is D $(8, 4 + \sqrt{17})$
Let the middle pt of chord be ( $t^{2}$ , 2t). Mid pt of chord must lie inside the ellipse
$\Rightarrow t^{4} + 8 t^{2} - 1 < 0 t^{2} ϵ (0, - 4 + \sqrt{17})$
eqn. of chord is $t^{2} x + 4 t y = t^{4} + 8 t^{2}$
$∴\propto ϵ (8, 4 + \sqrt{17})$